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  • Need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 31

Need solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.8 question 31

Answers (1)

Answer:

        log\left | log(sec\, x+tan\, x) \right |+C

Hint:

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

Given:

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

Explanation:

Let

        log(sec\, x+tan\, x)=t

        \frac{1}{sec\, x+tan\, x}(sec\, x\: tan\, x+sec^{2}x)dx=dt

        \Rightarrow \frac{\frac{sin\, x}{cos^{2}x}+\frac{1}{cos^{2}x}}{\frac{sin\, x}{cos\, x}+\frac{1}{cos\, x}}dx=dt

        \Rightarrow \frac{\frac{1+sin\, x}{cos^{2}x}}{\frac{1+sin\, x}{cos\, x}}dx=dt

        =sec\, xdx=dt

Put in (1)

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

        =log\left | log(sec\, x+tan\, x) \right |+C

Posted by

Gurleen Kaur

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