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Explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 32 maths

Answers (1)

Answer:

$log\left | log \: tan\frac{x}{2} \right |+C$

Hint:

$sin\, 2x=2sin\, x\, cos\, x$

Given:

$\int \! \frac{cos\, ecx}{log\, tan\frac{x}{2}}dx$ .....(1)

Explanation:

Let

$log\, tan\frac{x}{2}=t$

$\frac{1}{tan\frac{x}{2}}sec^{2}\frac{x}{2}(\frac{1}{2})dx=dt$

$\frac{1}{2cos\frac{x}{2}sin\frac{x}{2}}dx=dt$

$\frac{1}{sin2\times \frac{x}{2}}dx=dt$

$cos\, ecx\, dx=dt$

Put in (1)

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

$=log\left | log \: tan\frac{x}{2} \right |+C$

Posted by

Gurleen Kaur

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