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  • Need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 15

Need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 15

Answers (1)

Answer:

        log\left | log(tan\: x) \right |+C

Hint:

        tan\: x=\frac{sin\: x}{cos\: x},\: \: sec\: x=\frac{1}{cos\: x},\: \: cos\: ecx=\frac{1}{sin\: x}

Given:

        \int \! \frac{sec\: x\: cos\: ecx}{log\left ( tan\: x \right )}dx

Explanation:

Let

        log(tan\: x)=t

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

        \Rightarrow \frac{sec\: x}{\frac{sin\: x}{cos\: x}}\times \frac{1}{cos\: x}dx=dt

        \Rightarrow sec\: x\: cos\: ecx\: dx=dt

        =\int \! \frac{dt}{t}\: \: \: =log\: t+C

        =log\left | log(tan\: x) \right |+C

Posted by

Gurleen Kaur

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