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

Match List-I with List-II (where $c$ is an arbitrary constant)

Choose the correct answer from the options given below:

If $\int \frac{(1 + x \log x)}{xe^{-x}} dx = e^x f(x) + C$, where C is constant of integration, then $f(x)$ is

$\int_{0}^{1.5} [x] dx$, where $[x]$ denotes the greatest integer function $\leq x$, is equal to :

$\int \frac{\sqrt{\tan x}}{\sin x \cos x} dx$ equals :

$\int_{0}^{1} x^2 e^{x^3} \, dx$ is equal to :

$\int_0^2 (|x| + |x - 2|) dx =$