IB Mathematics Analysis and Approaches Question Type 4: Evaluating Integrals with an Inside Function and Its Derivative Exercises

Evaluate the integral $\int \sin (3x)dx$.

Evaluate the integral $\int \sin (x){\cos }^2(x)dx$.

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

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

Evaluate the integral $\int \frac{1}{x{\ln }^2(x)}dx$.

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

Evaluate the integral $\int \frac{2}{x(\ln (x){)}^3}dx$.

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

Evaluate the integral $\int \cos (2x)dx$.

Evaluate the integral $\int \frac{5x}{\sqrt{x^2+1}}dx$. [4 marks]

Evaluate the integral $\int x^3{e}^{x^4}dx$.

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

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

Evaluate the integral $\int \frac{\ln (x)}{x}dx$.