IB Mathematics Analysis and Approaches Question Type 3: Integrals with an Inside Function and Its Derivative Exercises

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

Evaluate the integral $\int \frac{1}{2\sqrt{x}}{e}^{\sqrt{x}}dx$.

Evaluate the integral $\int 5\cos (5x)dx$.

Evaluate the integral $\int \frac{x^3}{1+x^4}dx$.

Evaluate the integral $\int \frac{\sin x}{{\cos }^{3}x}dx$.

Evaluate the integral $\int {\sec }^2(x)\tan (x)dx$.

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

Evaluate the integral $\int 4x\sin (x^2)dx$.

Evaluate the integral $\int \frac{e^{2x}}{1+e^{2x}}dx$.

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

Evaluate the integral $\int (2x+3)(x^2+3x+1{)}^{5}dx$.

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