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Need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 27

Answers (1)

Answer:

        \frac{1}{2}log\left | x^{2}+sin\, 2x+2x \right |+C

Hint:

        \int\! \frac{1}{t}dt=log\left | t \right |+C

Given:

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

Explanation:

Let

        x^{2}+sin\, 2x+2x=t

        (2x+2cos\, 2x+2)dx=dt

        2(x+cos\, 2x+1)dx=dt

From (1)

        \frac{1}{2}\int \! \frac{dt}{t}=\frac{1}{2}log\left | t \right |+C

        =\frac{1}{2}log\left | x^{2}+sin\, 2x+2x \right |+C

Posted by

Gurleen Kaur

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