Question Type 4: Solving harder integrals with integration by parts Bootcamps

Evaluate the integral $\displaystyle\int x\ln x\,dx$.

Find $\displaystyle\int x^2\ln x\,dx$.

Compute $\displaystyle\int x\sin x\,dx$.

Find $\displaystyle\int(\ln x)^2\,dx$.

Compute $\displaystyle\int x^3\ln x\,dx$.

Evaluate $\displaystyle\int x^2\cos x\,dx$.

Compute $\displaystyle\int x^3e^x\,dx$.

Find $\displaystyle\int\arctan x\,dx$.

Evaluate $\displaystyle\int(\ln x)^3\,dx$.

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

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

Compute $\displaystyle\int x^2(\ln x)^2\,dx$.