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Question Number 141186 by SLVR last updated on 16/May/21

Commented by SLVR last updated on 16/May/21

$$Goodeveningsir..Mr.Dwaipayan..$$$$iforgottentowriteyourexplanation$$

Commented by SLVR last updated on 16/May/21

$$kindlyresendmeyoursolution$$$$takenwithintegrationbyparts$$$$please...$$

Commented by Ar Brandon last updated on 16/May/21

$$\mathrm{You}\mathrm{may}\mathrm{tap}\mathrm{your}\mathrm{username}\mathrm{to}\mathrm{sort}$$$$\mathrm{your}\mathrm{posts}$$

Commented by Ar Brandon last updated on 16/May/21

$$\mathrm{Q}139811$$

Answered by Ar Brandon last updated on 16/May/21

$$\mathcal{I}=\int \left(\frac{3\mathrm{sinx}+2}{{(2\mathrm{sinx}+3)}^2}\right)\mathrm{dx}$$$$=\int \left(\frac{{2\sin }^2\mathrm{x}+3\mathrm{sinx}+{2\cos }^2\mathrm{x}}{{(2\mathrm{sinx}+3)}^2}\right)\mathrm{dx}$$$$=\int \left(\frac{\mathrm{sinx}(3+2\mathrm{sinx})+\mathrm{cosx}\left(2\mathrm{cosx}\right)}{{(2\mathrm{sinx}+3)}^2}\right)\mathrm{dx}$$$$=-\int \mathrm{d}\left(\frac{\mathrm{cosx}}{3+2\mathrm{sinx}}\right)=-\frac{\mathrm{cosx}}{3+2\mathrm{sinx}}+\mathrm{C}$$

Commented by Ar Brandon last updated on 16/May/21

😉😃

Commented by SLVR last updated on 16/May/21

$$wow..mr.brandon...sir..igotitlengthy$$$$but...thisislovableandlucid..$$$$sogreat..sir$$

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