CALCULUS PRESENTED BY GUO CHENG GUANG（05-42）-- integral by parts

To do these four indefinite integrals we'll need to use integration by parts. This special rule, integral by parts , is derived from the product rule of derivative, is available for integrating products of two functions.Calculus--Indefinite Integrals (05-42, total: 305) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-41）-- integral by parts

Introduction to integration by Parts.The fact that this method come from the differential of function.. When working with the method of integral by parts,the differential of a function will be given first, and the function from which it come must be determined.

Calculus--Indefinite Integrals (combine together from 05-41,total:304) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-36-40）--Five Methods to Integrate

We used Five Different Integration techniques in this example and we got some different answers, but actually,they have the same answer in the end. We also can verify by differentiation. Why can we get different answers but all of answers are correct? Because each integration we use different constants for each integration and we play fast and loose with these constants of integral.So we need to be careful with the constants of integrtion, and remember we must understand that there are times where the constants of integral are important.

The Five Different Integration Techniques are:

1. Integral by Complex Variable With Factorization

2. Integral by Completing Square

3. Integral by Trigonometric Substitution

4. Integral by Complex Variable With Inverse Function

5. Integral by Gamma Function



The following methods have been used to solve this example:

1. Factarization

2. Partial Fraction

3. Integration of Trigonometric Integral

4. Euler's Formula

5. Expanding

6. Trigonometric Identities

-- Sum-difference Formulas

-- Double Angle Formula

7. Odd Function

8. Substitution

9. Inverse function

10. Logarithm Rules

11. Logarithmic Integral

12. Gamma function

Calculus--Indefinite Integrals (combine together from 05-36 to 05-40) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-40）--Integration by gamma function

Using gamma function solve integration.Calculus--Indefinite Integrals (05-40, total: 303) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG(05-39)--Integral by complex variab...

We used the following methods to solve the integration:

1. Factarization

2. Partial Fraction

3. Integration of Trigonometric Integral

4. Euler's Formula

5. Expanding

6. Trigonometric Identities-- Sum-difference Formulas

7. Odd Function

8. Substitution

9. Logarithm Rules

Calculus--Indefinite Integrals (05-39, total: 302) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-38）--Integration by Trigonometr...

We used the following methods to solve the integration:

1. Trigonometric Substitution

2. Completing Square

3. Double Angle Formula

4. Partial Fraction

5. Factarization

6. Logarithmic Integral

7. Integration of Trigonometric Integral

Calculus--Indefinite Integrals (05-38, total: 301) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-37)--Integration by completing ...

In this indefinite Integral, we used the following methods to solve the integration:

1. Trigonometric Substitution

2. Completing Square

3. Factarization

4. Partial Fraction

5. Double Angle Formula

6. Logarithmic Integral

7. Integration of Trigonometric Integral

Calculus--Indefinite Integrals (05-37, total: 300) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-36）-- Indefinite Integrate With...

Indefinite Integral with complex number. Calculus--Indefinite Integrals (05-36, total: 299) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-35）--three methods to integrate

Using three methods(1.Factorization+Partial Fraction 2.Factorization+Partial Fraction+Quadratic formula+Complex numble) 3.Factorization+Partial Fraction+Complex variable) to Solve Indefinite Integration. Calculus--Indefinite Integrals (05-35, total: 298) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG(05-34)--two methods to integrate

Using Factorization+Partial Fraction+Complex variable to Solve Indefinite Integration. Calculus--Indefinite Integrals (05-34, total: 297) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-33）

Using Factorization+Partial Fraction+Complex variable to Integrate. Calculus--Indefinite Integrals (05-32, total: 295) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-31）--Using Two Methods to solvi...

Using Two Methods (1.completing square, 2. quadratic formula with complex variable ) to solving Indefinite Integration in English.CALCULUS PRESENTED BY GUO CHENG GUANG (aged 11) and Guo Chengxi (aged 8) （05-31） Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-30）-- Using Two Methods of Inte...

Using Two Methods of Integration by Partial Fractions.Calculus--Indefinite Integrals (05-30, total: 293) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-29）--Integration Using Two Meth...

Integration Using Two Methods of Partial Fractions.Calculus--Indefinite Integrals (05-29, total: 292) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-28）--four methods for Indefinit...

Four methods for Indefinit Integrating.Calculus--Indefinite Integrals (05-28, total: 291) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-27）--- four ways to solve indef...

Four ways to Solve the Indefinite Integral.Calculus--Indefinite Integrals (05-27, total: 290) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-26）--Five methods to Solve the ...

Five methods to Solve the Indefinite Integral.

用5种方法解不定积分

Calculus--Indefinite Integrals (05-26, total: 289) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English.

在这个视频里，郭承光(11岁)和郭承曦(8岁)用英文讲解了微积分的不定积分(05-26, total: 289)。

Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

更多关于承光（11岁）和承曦（8岁）用英文开讲从小学到大学的数学和科学（物理，化学和生物）视频. 欢迎您来点评赐教。

https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-25）

Solve the Indefinite Integral with Complex variable.

Calculus--Indefinite Integrals (05-25, total: 288) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-24）

Calculus--Indefinite Integrals (05-24, total: 287) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-23）

Calculus--Indefinite Integrals (05-23, total: 286) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-22）

Calculus--Indefinite Integrals (05-22, total: 285) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-20）

Calculus--Indefinite Integrals (05-20, total: 283) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English.

Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（05-019）

Calculus--Indefinite Integrals (05-19, total: 282) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English.

Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw