Problems

01

Integration by parts - A and E

Compute the integral:

$$\int (2x+9)e^{x}dx$$

02

Integration by parts - A and T

Compute the integral:

$$\int x^2\sin xdx$$

03

Integration by parts - A and L

Compute the integral:

$$\int x^3\ln xdx$$

04

Integration by parts - A and E

Compute the integral:

$${\int }_0^{3}x{e}^{4x}dx$$

05

Integration by parts - A and I

Compute the integral:

$$\int {\tan }^{-1}(x)dx$$

06

Integration by parts - E and T, “breaking the circle”

Compute the integral:

$$\int e^x\sin (x)dx$$

You should perform IBP twice, find an equation, and use algebra to solve it (“breaking the circle”) for the desired integral.