$\int_{\pi / 5}^{3 \pi / 10} \frac{d x}{\sec ^2 x+\left(\tan ^{2022} x-1\right)\left(\sec ^2 x-1\right)}=$

If $a > 0$, then $\int_{-\pi}^{\pi} \frac{\sin^2 x}{1+a^x} dx$ is equal to

The true set of values of $a$ for which the inequality $\int_{a}^{0} (3^{-2x} - 2 \cdot 3^{-x}) \, dx \geq 0$ is true is:

If $\int_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x \, dx}{(1+e^{\sin x})(1+\sin ^4 x)} = \alpha \pi + \beta \log _e(3+2 \sqrt{2})$,where $\alpha, \beta$ are integers,then $\alpha^2+\beta^2$ equals.....................

The value of the integral $\int_{-2}^0 (x^3 + 3x^2 + 3x + 5 + (x + 1) \cos(x + 1)) \, dx$ is equal to:

Evaluate $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} f(x) dx$,where $f(x) = \sin |x| + \cos |x|$ for $x \in [-\frac{\pi}{2}, \frac{\pi}{2}]$.