Question Type 3: Integrals with an inside function and its derivative Exercises

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

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

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

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

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

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

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

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

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

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

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

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