$\int \cos^{-3/7} x \sin^{-11/7} x \, dx = $

If $\int \frac{\sin x \cos x}{\sqrt{\cos^4 x - \sin^4 x}} dx = -\frac{f(x)}{2} + c$,then the domain of $f(x)$ is

$\int \frac{25 x^2+8}{\sqrt{25 x^2+9}} d x=$

If $I_n = \int \tan^n x \, dx$ $(n > 1)$,then $I_4 + I_6 =$

If $\int \sqrt{\frac{2}{1+\sin x}} dx = 2 \log |A(x) - B(x)| + C$ and $0 \leq x \leq \frac{\pi}{2}$,then $B(\frac{\pi}{4}) = $

If $\int\left(\frac{1}{x}+\frac{1}{x^3}\right)\left(\sqrt[23]{3 x^{-24}+x^{-26}}\right) d x =-\frac{\alpha}{3(\alpha+1)}\left(3 x^\beta+x^\gamma\right)^{\frac{\alpha+1}{\alpha}}+C, x>0,$ $(\alpha, \beta, \gamma \in Z)$,where $C$ is the constant of integration,then $\alpha+\beta+\gamma$ is equal to . . . . . . .