Question
$\int_0^\pi {x\sin x\,dx = } $
==> $2I = \pi \int_0^\pi {\sin xdx = \pi [ - \cos x]_0^\pi \Rightarrow I = \pi } $.
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$\int\left(\left(\frac{x}{e}\right)^{2 x}+\left(\frac{e}{x}\right)^{2 x}\right) \log _e x d x=\frac{1}{\alpha}\left(\frac{x}{e}\right)^{\beta x}-\frac{1}{\gamma}\left(\frac{e}{x}\right)^{\delta x}+C$
है, जहाँ $\mathrm{e}=\sum_{\mathrm{n}=0}^{\infty} \frac{1}{\mathrm{n} !}$ तथा $\mathrm{C}$ समाकलन अचर है, तो $\alpha+2 \beta+3 \gamma-4 \delta$ बराबर है