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Explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 24 maths

Answers (1)

Answer:

$log\left | log\: sin\: x \right |+C$

Hint:

$cot\: x=\frac{cos\: x}{sin\: x}$

Given:

$\int\! \frac{cot\: x}{log\: sin\: x}dx$ ........(1)

Explanation:

Let

$log\: sin\: x=t$

$\frac{1}{sin\: x}(cos\: x)dx=dt$

$cot\: x\: dx=dt$

Put in (1)

$\int\! \frac{dt}{t}=log\left | t \right |+C$

$=log\left | log\: sin\: x \right |+C$

Posted by

Gurleen Kaur

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