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  • Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 37 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 37 maths textbook solution

Answers (1)

Answer:

        log\left | x+log\, sec\, x \right |+C

Hint:

        Put denominator = t

Given:

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

Explanation:

Let

        x+log\, sec\, x=t

        [1+\frac{1}{sec\, x}(sec\, x\, tan\, x)]dx=dt

        (1+tan\, x)dx=dt

Put in (1)

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

        =log\left | x+log\, sec\, x \right |+C

Posted by

Gurleen Kaur

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