$\int_{-\pi}^{\pi} (1-x^2) \sin x \cdot \cos^2 x \, dx$ ની કિંમત શોધો.

સંકલન $\int_0^{\infty} \frac{dx}{(1+x^2)(1+x)^2}$ નું મૂલ્ય છે

$\int_0^{\pi / 2} \frac{\sin ^3 x \cos x \, dx}{\sin ^4 x+\cos ^4 x} = ?$

$\sum_{r=1}^{20} \left( \sqrt{\pi \left( \int_0^r x |\sin \pi x| dx \right)} \right)$ નું મૂલ્ય . . . . . . છે.

જો $I_n = \int_{-\pi}^{\pi} \frac{\sin(nx)}{(1+\pi^x) \sin x} dx$,$n=0, 1, 2, \ldots$,હોય,તો
$(A)$ $I_n = I_{n+2}$
$(B)$ $\sum_{m=1}^{10} I_{2m+1} = 10\pi$
$(C)$ $\sum_{m=1}^{10} I_{2m} = 0$
$(D)$ $I_n = I_{n+1}$

$\int_{\frac{\pi}{4}}^{\frac{5 \pi}{4}} (|\cos t| \sin t + |\sin t| \cos t) dt =$