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Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.8 question 21 maths textbook solution

Answers (1)

Answer:

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

Hint:

        \frac{\mathrm{d} }{\mathrm{d} x}(x+cos\, x)=1-sin\, x

Given:

        \int \! \frac{1-sin\, x}{x+cos\, x}dx

Explanation:

Let

        x+cos\; x=t

        (1-sin\, x)dx=dt

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

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

Posted by

Gurleen Kaur

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