જો $\int \frac{5 \tan (x)}{\tan (x)-2} d x = x + a \log |\sin (x) - 2 \cos (x)| + k$ હોય,તો $a$ ની કિંમત શોધો.

વિધેયનું સંકલન કરો: $\frac{1}{\sqrt{(x-1)(x-2)}}$

$\int \frac{1}{x^5 \sqrt[5]{x^5+1}} d x=$

$\begin{aligned} & \int \frac{x \, dx}{\sqrt[15]{\left(1+x^2\right)^{12}\left(2+x^2\right)^{18}}}=\alpha\left(\frac{1+x^2}{2+x^2}\right)^{1 / n}+C \Rightarrow \\ & \frac{n}{\alpha}= \end{aligned}$

$I_n = \int \frac{t^n}{1+t^2} dt, (n = 1, 2, 3, \ldots) \Rightarrow I_6 + I_4 =$

જો $\int \frac{1}{\cos 4x \cos 2x} dx = \frac{1}{2\sqrt{2}} \log \left(\frac{1+f(x)}{1-f(x)}\right) - \frac{1}{2} \log g(x) + C$ હોય,તો $g\left(\frac{\pi}{6}\right) - \sqrt{2} f\left(\frac{\pi}{6}\right)$ ની કિંમત શોધો.