IB Mathematics Analysis and Approaches Question Type 1: Solving Harder Integrals with U-substitution Exercises

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

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

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

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

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

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

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

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

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

Find $\int {\sin }^3(x)\cos (x)dx$.

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

Compute $\int x(x^2+5{)}^{3}dx$.