$\int \frac{1}{x^2+4x+8}dx$ is equal to (Where C is an arbitrary constant)

Value of $\int_{1}^{4} \frac{\log_e x}{x^2}\, dx$ is

If $I = \int \frac{x^4 + x^2 + 1}{x^2 - x + 1} dx = \alpha x + \beta x^2 + \gamma x^3 + \delta$, $\delta$ is constant of integration, then $(\alpha + 2\beta + 3\gamma)$ equals

The value of $\int_{-1}^{1} \dfrac{x^6}{6^x+1}\,dx$ is

$\int_0^{4\pi} \frac{x}{1 + |\cos x|} dx =$

The value of $\int_{0}^{\pi/2} \frac{\tan^7 x}{\cot^7 x + \tan^7 x} dx$ is

$\int_{1}^{5} |x - 2| \, dx =$