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

$\int \mathrm{e}^{\mathrm{x}}\left(\frac{2 \mathrm{x}+1}{2 \sqrt{\mathrm{x}}}\right) \mathrm{dx}$

$\int \frac{dx}{(a^2-x^2)^{3/2}}$ is equal to: (where C is an arbitrary constant)

The value of the integral $\int_{-6}^{0} |x+3|\,dx$ is

If the manufacturer's marginal cost function is $100\left(\frac{1}{\sqrt{x}}+50\right)$, then the cost involved to increase production from 25 units to 100 units is:

$\int\frac{\tan^5\sqrt{x}.\sec^2\sqrt{x}}{\sqrt{x}}dx$ is equal to:

$\int\frac{x-1}{x(x-\log x)}dx$ equals:

(consider: $\log x=\log_e x$)