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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 24

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 24

Answers (1)

Answer:\log|\log(\sin x)|+c

Hints: You must know about the integral rule of logarithm and trigonometric functions

Given: \int \frac{\cos x}{\sin x\log \sin x}dx

Solution:\log \sin x =t     and differentiate both sides, \left [ \frac{d}{dx} \log \sin x=\frac{1}{\sin x}.\frac{d}{dx}\sin x\right ]

\begin{aligned} &\frac{1}{\sin x} \cdot \cos x=d t \\ &\int \frac{\cos x d x}{\sin x \cdot \log \sin x}=\int \frac{d t}{t} \\ &\log |t|+c \\ &\log |\log (\sin x)|+c \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\left[\int \frac{1}{x} d x=\log x+c\right] \end{aligned}   

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