$\displaystyle\int \dfrac{x^3}{x+2}dx$ is equal to: (where $C$ is an arbitrary constant and $\log_e x = \log x$)

$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{dx}{1 + \sqrt{tanx}}$ is equal to

$\displaystyle\int x\sqrt{x^2-1}\,dx$ is equal to : ( where C is an arbitrary constant )

$\int_{-1}^1 \frac{x^3 + |x| + 1}{x^2 + 2|x| + 1}dx$ is equal to

If $f(a-x) = f(x)$, then $\int_0^a xf(x)dx$ is equal to

The value of the definite integral $\int_0^1 e^x \frac{(1-x)^2}{(1+x^2)^2}dx$ is:

$\displaystyle\int e^{x\log_e 7} e^x\, dx$ is equal to :

[where C is an arbitrary constant]