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Need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 51

Answers (1)

Answer:

        sec\, x+log\left | tan\frac{x}{2} \right |+C

Hint:

        sin^{2}x+cos^{2}x=1

Given:

        \int \! \frac{1}{sin\, x\, cos^{2}x}dx

Explanation:

        \int \! \frac{sin^{2}x+cos^{2}x}{sin\, x\, cos^{2}x}dx

        =\int \! \frac{sin^{2}x}{sin\, x\, cos^{2}x}dx+\int \! \frac{1}{sinx}dx

        =\int \! tan\, xsec\, xdx+\int \! cos\, e\, cxdx

        =sec\, x+log\left | tan\frac{x}{2} \right |+C

Posted by

Gurleen Kaur

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