Mathematics

# Solve :$\int x^{ \sin x} \left( \dfrac {sinx}{x} + \cos x . logx \right) dx$

##### SOLUTION
$\begin{array}{l} \int { { x^{ \sin x } }\left( { \frac { { \sin x } }{ x } +\cos x\log x } \right) } dx \\ y={ x^{ \sin x } } \\ \log y=\sin x\log x \\ \frac { 1 }{ y } \frac { { dy } }{ { dx } } =\cos x\log x+\frac { { \sin x } }{ x } \\ \frac { { dy } }{ { dx } } ={ x^{ \sin x } }\left[ { \cos x{ { logx } }+\frac { { \sin x } }{ x } } \right] \\ \int { dy } =y+C \\ ={ x^{ \sin x } }+C \end{array}$
Hence,
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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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