IB Mathematics Analysis and Approaches Question Type 4: Solving Harder Integrals with Integration by Parts Exercises

Evaluate $\int x^2\cos xdx$.

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

Evaluate the integral $\int x\ln xdx$.

Find $\int \arctan xdx$.

Find $\int x\sin x\mathrm{d}x$.

Evaluate $\int (\ln x{)}^{3}dx$.

Compute $\int x^2(\ln x{)}^{2}dx$.

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

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

Evaluate $\int \frac{\ln x}{x^2}dx$.

Evaluate $\int x^2{e}^{2x}dx$.

Find $\int (\ln x{)}^{2}dx$.