Loooong time no see!!

It has been a long time since I have logged in the forum. Here I have brought back a few integrals for you :)

1) $\displaystyle\int \dfrac{\tan^3\theta \sec\theta \; d\theta}{\sqrt{\tan^2\theta + 2}}$

2) $\displaystyle \int \dfrac{\sec(2\theta)\cdot(\cos \theta - \sin \theta)^2\;d\theta}{\sqrt{1+\sin (2\theta)}}$

3)$\displaystyle\int\left(\sqrt{\cot x}-\sqrt{\tan x}\right)dx$

4) $\displaystyle \int\left(x^{x+1}(\ln x + 1)^2-x^x\right)dx$

5) $\displaystyle\int \sqrt{\tanh x}\; dx$

6) $\displaystyle \int \sqrt[3]{\tan x}\; dx$

7) $\displaystyle \int \dfrac{1+\sin\theta + \cos \theta}{1-\sin\theta + \cos \theta}d\theta$

8) $\displaystyle \int \dfrac{x^3}{\sqrt{x^8+1}}dx$

Good luck solving those :P

Integrals are really fun :D

~The smartest cookie in the world :P

And I'm a real cookie :P

Edited: Hehe 1 more:

9) $\displaystyle \int \sqrt{\cot x}dx$