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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 7

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Answer:\frac{1}{2}\log \left | 3+2\sin x \right |+c

Hint: You must know about the integration rule of sin and cos function.

Given: \int \frac{\cos x}{3+2\sin x}dx


Let \sin x=t       differentiate both sides,  \left [ \frac{d}{dx}\sin x= \cos x \right ]

\cos x dx=dt

I=\int \frac{dt}{3+2t}

\left (\frac{1}{2} \right )\log \left ( 3+2t \right )+c                                                                    \left [ \int \frac{1}{2x} dx=\frac{1}{2}\log 2x +c\right ]

= \frac{1}{2}\log \left | 3+2\sin x \right |+c                                                  


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