If $\int e^u \sin 2x \, dx$ can be expressed in terms of elementary functions of $x$,then $u$ can be:

$\int \frac{\sqrt{\cos 2 x}}{\sin x} d x=$

$\int \frac{2-\sin x}{2 \cos x+3} d x=$

For real numbers $\alpha, \beta, \gamma$ and $\delta,$ if $\int \frac{\left(x^{2}-1\right)+\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)}{\left(x^{4}+3 x^{2}+1\right) \tan ^{-1}\left(\frac{x^{2}+1}{x}\right)} d x =\alpha \log _{e}\left(\tan ^{-1}\left(\frac{x^{2}+1}{x}\right)\right) +\beta \tan ^{-1}\left(\frac{\gamma\left(x^{2}-1\right)}{x}\right)+\delta \tan ^{-1}\left(\frac{x^{2}+1}{x}\right)+C$ where $C$ is an arbitrary constant,then the value of $10(\alpha+\beta \gamma+\delta)$ is equal to ....... .

The value of $\int \frac{d x}{(x+1)^{3 / 4}(x-2)^{5 / 4}}$ is equal to

$\int \sqrt{\frac{1+x}{1-x}} \, dx = $