Question Type 1: Solving harder integrals with u-substitution Bootcamps

Integrate $\int \frac{2x}{4 + x^2}\,dx$.

Compute $\displaystyle \int x\,(x^2 + 5)^3\,dx$.

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

Compute $\displaystyle \int \frac{6x}{\sqrt{1 + 3x^2}}\,dx$.

Find $\displaystyle \int \frac{e^{2x}}{1 + e^{2x}}\,dx$.

Evaluate $\displaystyle \int 3x^2\,(2 + x^3)^4\,dx$.

Find $\displaystyle \int \sin^3(x)\cos(x)\,dx$.

Evaluate $\displaystyle \int \frac{4x^3}{(1 + x^4)^2}\,dx$.

Evaluate $\displaystyle \int \frac{x^2}{x^3 + 1}\,dx$.

Compute $\displaystyle \int \frac{2x}{4 + x^4}\,dx$.

Evaluate $\displaystyle \int \frac{x^5}{(x^6 + 1)^2}\,dx$.

Compute $\displaystyle \int \frac{1}{x\,\bigl(\ln x\bigr)^2}\,dx$.