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Question Number 138810 by mathdanisur last updated on 18/Apr/21

∫_( 0) ^( π/2) ((xsin(x))/(1−cosx))∙log(1+cosx)dx=?

$$\underset{\:\mathrm{0}} {\overset{\:\pi/\mathrm{2}} {\int}}\frac{{xsin}\left({x}\right)}{\mathrm{1}−{cosx}}\centerdot{log}\left(\mathrm{1}+{cosx}\right){dx}=? \\ $$

Answered by phanphuoc last updated on 18/Apr/21

u=x,dv=ln(1+cosx)dcosx/(1−cosx)

$${u}={x},{dv}={ln}\left(\mathrm{1}+{cosx}\right){dcosx}/\left(\mathrm{1}−{cosx}\right) \\ $$

Commented by mathdanisur last updated on 18/Apr/21

Sir, the exact solution

$${Sir},\:{the}\:{exact}\:{solution} \\ $$

Commented by mathdanisur last updated on 21/Apr/21

please sir continued

$${please}\:{sir}\:{continued} \\ $$

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