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  • Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.16 question 2

Provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.16 question 2

Answers (1)

Answer:

        tan^{-1}(e^{x})+C

Hint:

Use substitution method as well as special integration formula to solve this type of problem

Given:

        \int \frac{e^{x}}{1+e^{2x}}dx

Solution:

Let\: \: I=\int \frac{e^{x}}{1+e^{2x}}dx

Put\: \: e^{x}=t\Rightarrow e^{x}dx=dt

Then\: \: I= \int \frac{1}{1+t^{2}}dx

        \begin{array}{ll} =\tan ^{-1}\left(\frac{t}{1}\right)+C & {\left[\because \int \frac{1}{a^{2}+x^{2}} d x=\frac{1}{a} \tan ^{-1}\left(\frac{x}{a}\right)+C\right]} \\ \\ =\tan ^{-1}\left(e^{x}\right)+C \quad & {\left[\because t=e^{x}\right]} \end{array}

Posted by

Gurleen Kaur

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