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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 17

Answers (1)

Answer:

\log \left|e^{x}+1\right|+c

Hint:

Simplify it and integrate it.

Solution:

I=\int \frac{e^{x}}{e^{x}+1} d x

Let e^{x}+1 =y            …(i)

\begin{aligned} &\Rightarrow e^{x} d x=d y \\ &\Rightarrow I=\int \frac{d y}{y} \end{aligned}

\begin{aligned} &I=\log |y|+c \\ &I=\log \left|e^{x}+1\right|+c \end{aligned}         …from equi (i)

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