Integration Techniques and Anti-Derivatives

Trigonometric substitution

Table of integrals

Partial fraction decomposition

Integration by parts

1 / a * (U - 1) * e^(aU) + C

a^2 * U * e^(aU) + C

U * e^(aU) + C

1 / a^2 * (Au - 1) * e^(Au) + C

To change the variable of integration

To eliminate the need for substitution

To simplify the integration process

To make the integral more complex

5

6

4

3

Because U is already integrated

Because U is not present

Because U is equal to X

Because U is a constant

6/5 * (x - 1) * e^(5x) + C

6/25 * (x - 1) * e^(5x) + C

6/5 * (5x - 1) * e^(5x) + C

6/25 * (5x - 1) * e^(5x) + C

5/6 x

5/3 x

3/5 x

6/5 x

6/5 x * e^(5x) + 6/25 e^(5x) + C

6/25 x * e^(5x) + 6/5 e^(5x) + C

6/25 x * e^(5x) - 6/5 e^(5x) + C

6/5 x * e^(5x) - 6/25 e^(5x) + C

5/6 x - 25/30 e^(5x) + C

6/25 x - 5/6 e^(5x) + C

25/30 x - 5/6 e^(5x) + C

30/25 x - 6/25 e^(5x) + C

6/5 x * e^(5x) - 6/25 e^(5x) + C

6/25 x * e^(5x) - 6/5 e^(5x) + C

6/5 x * e^(5x) + 6/25 e^(5x) + C

6/25 x * e^(5x) + 6/5 e^(5x) + C