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:

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

$\int e^{(x \log 5)}e^x dx$, is:

Where $C$ is the constant of integration.

$\int \frac{(x^4 - x)^{1/4}}{x^5} dx$ is equal to

If $\int \frac{\sin^6 x}{\cos^{10} x}\,dx = -2a\tan^9 x + b\tan^7 x + c$, (where c is an arbitrary constant), then which one of the following is TRUE?

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

$\int \frac{x^8}{(x^3+1)^{1/3}} dx$ is equal to