∫x sinx $$sec3x$$ dx $$=$$

Question

∫x sinx $$sec3x$$ dx $$=$$

Infinity Learn · Accepted Answer

∫x sinx $$sec3x$$ dx​$$=$$∫x sinx $$.1cos3x$$ dx​                                  $$=$$∫x tanx $$sec2x$$ dx​                                              integration by parts, let $$u=x$$ and $$v=tanx$$ $$sec2x$$                                   ​$$=x$$ ∫$$sec$$ xtanx secx dx−∫$$sec$$ xtanx secx dxdx​                                  $$=xsec2x2$$−∫$$sec2x2dx$$                                  ​$$=xsec2x2$$−$$tanx2+c$$

$\int x \sin x s e c^{3} x d x =$

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∫x sinx sec3x dx =

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$\int x \sin x s e c^{3} x d x =$