Practice questions for Integration.

1). \(\displaystyle \int (x^{\frac{2}{3} }+1) dx\)

2). \(\displaystyle \int \frac{1-\sin x}{\cos^{2}x} dx\)

3).\(\displaystyle \int \displaystyle\left( \sqrt{x} +\frac{1}{\sqrt{x}}\right)dx \)

4).\(\text{Find } \;\; \displaystyle f(x)\;\; \text{if} \;\;\displaystyle f'(x)=4x^3-\frac{3}{x^4}\;\;\) \(\text{ such that}\;\; f(2)=0\)

5).\(\displaystyle \int \frac{\tan^{4}\sqrt{x} . \sec^{2} \sqrt{x}}{\sqrt{x}}dx\)

\(\text{HINT-Put} \sqrt{x}=t\)

6).\( \displaystyle \int 2x\sin(x^2+1)dx\)

7).\(\displaystyle \int\frac{(\log x)^2}{x} dx \)

8).\( \displaystyle \int (x^3-1)^{\frac{1}{3}} x^5 dx\)

9).\(\displaystyle \int \frac{x}{e^{x^2}}dx\)

10).\( \displaystyle \int \frac{dx}{\sin^{2}x.\cos^{2}x}\)