Assignments

This series of assignments applies substitution as a way to find the primitive function of an integral.

1. Solve:

$\displaystyle\int{(5x+2)^{10}}dx$

2. Solve:

$\displaystyle\int{5(2x+10)^3}dx$

3. Solve:

$\displaystyle\int{\displaystyle\frac{1}{4}e^{2x+1}}dx$

4. Solve:

$\displaystyle\int_{2}^{3}{\displaystyle\frac{1}{3x+1}}dx$

5. Solve:

$\displaystyle\int_{0}^{\pi}\cos(2x)dx$

6. Solve:

$\displaystyle\int{\displaystyle\frac{2x+1}{4x^2-1}}dx$

7. Solve:

$\displaystyle\int_{0}^{\pi}{[2\cos^2(x)-1]}dx$

8. Solve:

$\displaystyle\int_{0}^{1}{[(3x+1)^2-(3x-1)^2]}dx$

9. Solve:

$\displaystyle\int{\displaystyle\frac{1}{(6x+4)^2}}dx$

10. Solve:

$\displaystyle\int{\sqrt{3x+1}}dx$