$$ \int \frac{d x}{x \ln (x) \ln ^2(x) \ln ^3(x) \ldots \ln ^m(x)}=\frac{(\ln (x))^K}{K}+C \Rightarrow 2 K= $$

If $I_m=\int x^m \cos n x d x=g(x)-\frac{m(m-1)}{n^2} I_{m-2}$, then $g(x)=$

Let $I_n=\int \sec ^n x d x$. If $5 I_6-4 I_4=f(x)$, then $f\left(\frac{\pi}{4}\right)$ is equal to

If $\int e^{\sin ^2 x}\left(\sin x \cos x+\cos ^3 x \sin x\right) d x=e^{\sin ^2 x}(1+f(x))+c$, then $f^{\prime}(x)=$