Mathematics

# $\int \dfrac{\cos x}{(1+\sin x)(2+\sin x)}dx$

##### SOLUTION
We have,
$\int \dfrac{\cos x}{(1+\sin x)(2+\sin x)}dx$

Let $y=1+\sin x$
$dy=\cos x.dx$

Therefore,
$\Rightarrow\int\dfrac{dy}{y(1+y)}=\int\dfrac{(1+y)-y}{y(1+y)}dy$
$\Rightarrow\int\left(\dfrac{1}{y}-\dfrac{1}{1+y}\right)dy$
$\Rightarrow \ln (y)-\ln (1+y)+c$
$\Rightarrow \ln(1+\sin x)-\ln(2+\sin x)+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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