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Question

Mathematics Question on integral

Integrate the function: cos3x elog sin xcos^3 x\ e^{log\ sin\ x}

Answer

cos3x elog sin xcos^3 x\ e^{log\ sin\ x} = cos3x.sin xcos^3x . sin\ x

Let cosx=t⇒−sin x dx=dtLet \ cos x=t ⇒ -sin \ x\ dx=dt

⇒$$∫$$cos^3 x\ e^{log\ sin\ x}\ dx = ∫cos3x sin x dx∫cos^3x\ sin\ x\ dx

                                  =$-∫t.dt$

                                  =$-\frac {t^4}{4}+C$

                                  =$-\frac {cos^4x}{4}+C$