Question

Integrate :

Answer 1

\[\huge \int\limits_{\frac{1}{\sqrt{2}}}^{\frac{\sqrt{3}}{2}} \ln e^{\cos x}d(\sin x)\]

Answer 2

@ash2326 @Hero @Luigi0210 @Callisto @robtobey @dan815

Answer 3

Substitute \(u=\cos x\), so \(du=-\sin x ~dx~\iff~-du=d(\sin x)\), if I'm interpreting the notation correctly.

Answer 4

Or you can simply say
\[\ln e^{\cos x}=\cos x\ln e=\cos x\]