The value of the integral $\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x$ is

If $[x]$ denotes the greatest integer less than or equal to $x$,then the value of the integral $\int_{-\pi / 2}^{\pi / 2} [[x] - \sin x] \, dx$ is equal to:

The value of $\int_0^\pi {{e^{{{\cos }^2}x}}{{\cos }^5}3x} \,dx$ is

$\int_{0}^{\frac{\pi}{2}} \frac{\sin^{\frac{2}{3}} x}{\sin^{\frac{2}{3}} x + \cos^{\frac{2}{3}} x} dx =$

If $I_{n+1} = \int_{0}^{1} \frac{x^{n+1} - 1}{x + 1} dx$,then the value of $I_{10} + I_{11} + 2 \log 2$ is:

If $g(x) = \int_0^x \cos^4 t \,dt$, then $g(x+\pi)$ equals