The sum to infinite terms of the series $\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{2}{9}\right)+\ldots \ldots . .+\tan ^{-1}\left(\frac{2^{n-1}}{1+2^{2 n-1}}\right)+\ldots \ldots$. is

The ratios of sides in a triangle ABC are $5: 12: 13$ and its area is 270 . Then sides of the triangle are

If $4 \sin ^{-1} x+\cos ^{-1} x=\pi$ then $x=$

$$\int_1^e \frac{\mathrm{e}^x}{x}(1+x \log x) \mathrm{d} x=$$