Question Type 4: Evaluating integrals with an inside function and its derivative Exercises

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

Evaluate the integral $\displaystyle \int \sin(x)\cos^2(x)\,dx$.

Evaluate the integral $\displaystyle \int \tan(x)\sec^2(x)\,dx$.

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

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

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

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

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

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

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

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

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

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

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