$\int_{-\pi}^{\pi} x^2 \sin x \, dx =$

Value of the definite integral,$\int\limits_{ - \frac{1}{2}}^{\frac{1}{2}} {\,(\,\,{{\sin }^{ - 1}}(3x - 4{x^3})\,\, - \,\,{{\cos }^{ - 1}}(4{x^3} - 3x)\,\,)\,dx} \,\,$

The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(x^3+\cos x+\tan^5 x) dx$ is equal to . . . . . . .

The value of the integral $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \left(x^2 + \log \frac{\pi-x}{\pi+x}\right) \cos x \, dx$ is equal to

If $\int_0^{2024 \pi} \frac{2023^{\sin ^2 x}}{2023^{\sin ^2 x}+2023^{\cos ^2 x}} d x=k$,then $\left(\frac{2 k}{\pi}+1\right)=$

If $\int_0^{\frac{\pi}{2}} \log \cos x \, dx = \frac{\pi}{2} \log \left(\frac{1}{2}\right)$,then $\int_0^{\frac{\pi}{2}} \log \sec x \, dx = $