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Write a Value of ∫ E Log S I N X Cos X D X - Mathematics

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Sum

Write a value of

\[\int e^{\text{ log  sin x  }}\text{ cos x}. \text{ dx}\]
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Solution

Let Ielog sin x . cos x dx 

\[\int\] sin x × cos x dx            \[\left( \because e^{log \text{ a} }= a \right)\]
Let sin t
⇒​ cos x dx = dt
\[\therefore I\]\[\int\] t . dt

\[= \frac{t^2}{2} + C\]
\[ = \frac{\sin^2 x}{2} + C \left( \because t = \sin x \right)\]

Concept: Methods of Integration: Integration by Substitution
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Very Short Answers | Q 11 | Page 197
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