IB Mathematics Analysis and Approaches Question Type 3: Solving Simple Integrals with Integration by Parts Exercises

Find the integral

$$\int {\ln }^{2}xdx$$

Compute the integral

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

Evaluate the integral

$$\int \ln (x+1)dx$$

Find the integral:

$$\int x^2{e}^{3x}dx$$

Evaluate the integral

$$\int x\cos xdx$$

Evaluate the integral

$$\int \ln (4x)dx$$

Compute the integral

$$\int x{e}^{x}dx$$

Compute the integral

$$\int \arctan xdx$$

Evaluate the integral

$$\int x^2\ln xdx$$

Find the integral

$$\int x^3{e}^{5x}dx$$

Find the integral

$$\int x\ln (2x)dx$$

Find the integral

$$\int e^{2x}\sin (3x)dx$$

Find the area under $f(x)=\arctan (x)$ from $x=0$ to $x=1$.