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