The integral $I = \int \frac{(1+\log_e x)^3}{x} dx$ is equal to

If $\dfrac{d}{dx}[f(x)] = 5x^4 - \dfrac{2}{x^3}$ such that $f\left(-\dfrac{1}{2}\right) = 0$, then $f(x)$ is equal to

If $\int_0^{\pi/2} \sqrt{\tan x} \, dx = \frac{\lambda}{\sqrt{2}}$, then the value of $\lambda$ is

$\int 3x^2 e^{x^3}\,dx$ is equal to : (where $C$ is an arbitrary constant)

The value of integral $\int \sqrt{4x^2 + 9}\, dx$ is

$\displaystyle\int e^x(\sec x + \log_e(\sec x + \tan x))dx$ is equal to: (where C is an arbitrary constant)

$\int \frac{dx}{x(x^{10}+1)}$ is equal to