If $g(x) = \int \frac{dx}{x^{1/2} + x^{1/6}}$, then $g(1) - g(0)$ 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

Let $[t]$ denotes the greatest integer $\le t$, then the value of $\left[\displaystyle\int_{\pi}^{3\pi/2} x|\sin x|\,dx\right]$ is:

$\displaystyle\int \dfrac{1}{(x-1)^{3/4}(x+2)^{5/4}}\, dx$ is equal to :

[where C is an arbitrary constant]

For $x \neq -1$, if $\int \frac{xe^x dx}{(1+x)^2} = \frac{ae^x}{(1+x)^b} + c$, where a, b are fixed numbers and c is the integration constant, then $a + b$ is equal to

$\int \frac{dx}{9x^2 - 16}$ is equal to

If $\int_0^a 3x^2dx = 8$, then the value of $a$ is: