The value of $\displaystyle\int_{-1}^{1}|x^4-x|\,dx$ is equal to:

The value of $\int_{-2}^{3} |x-1|\, dx$ is

For $x \in \left(0, \frac{\pi}{2}\right)$, $\int \frac{1}{\sin^2 x + \sin 2x} dx$ is equal to

$\int \frac{x}{(x-1)(x-2)} dx$ is equal to ( where $C$ is a constant of integration)

$\displaystyle\int \dfrac{xdx}{x^2+3x+2}$ is equal to:

(where $c$ is an arbitrary constant)

The value of integral $\int_{-\pi/2}^{\pi/2} \frac{1}{1+e^{\sin x}}dx$ is

$\int \left(\frac{1}{log_e t} - \frac{1}{(log_e t)^2}\right) dt$ is equal to