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Q.

Find ∫esinxxcos3x-sinxcos2xdx

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a

xesinx-esinxsecx+C

b

xecosx-esinxsecx+C

c

x2esinx+esinxsecx+C

d

2xesinx-esinxtanx+C

answer is A.

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Detailed Solution

∫esinxxcos3x−sinxcos2xdx=∫esinxxcosxdx−∫esinxtanxsecxdx                              =∫xdesinx−∫esinxd(secx)                                                                              =xesinx−∫esinxdx−esinxsecx−∫esinxsecxcosxdx                    =xesinx−esinxsecx+C
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Find ∫esinxxcos3x-sinxcos2xdx