Mathematics

# Write a value of $\int { { e }^{ \log { \sin { x } } }\cos { x } } dx$

##### SOLUTION
Let $t=\sin{x}\Rightarrow\,dt=\cos{x}dx$

$I=\displaystyle\int{{e}^{\log{\sin{x}}}\cos{x}dx}$

$=\displaystyle\int{{e}^{\log{t}}dt}$

$=\displaystyle\int{t\,dt}$

$=\dfrac{{t}^{2}}{2}+c$    .......where $c$ is the constant of integration.

$=\dfrac{{\sin}^{2}{x}}{2}+c$    .......where $t=\sin{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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