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Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 41 maths textbook solution

Answers (1)

Answer:

        log\left | tan\, x+2 \right |+C

Hint:

        \frac{\mathrm{d} }{\mathrm{d} x}(tan\, x)=sec^{2}x

Given:

        \int \! \frac{sec^{2}x}{tan\, x+2}dx                            ....(1)

Explanation:

Let

        tan\, x+2=t

        sec^{2}xdx=dt

Put in (1)

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

                  =log\left | tan\, x+2 \right |+C

Posted by

Gurleen Kaur

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