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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 50

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 50

Answers (1)

Answer: e^{\tan^{-1}x}+c

Hints: You must know about the integral rule of exponential and trigonometric functions.

Given: \int \frac{e^{\tan^{-1}x}}{1+x^{2}}dx

Let\tan^{-1}x =t and differentitate on both sides,

\begin{aligned} &\frac{1}{1+x^{2}}=\frac{d t}{d x} \\ &d x=\left(1+x^{2}\right) d t \\ &\int \frac{e^{t}}{1+x^{2}} \cdot\left(1+x^{2}\right) d t \\ &\int e^{t} d t=e^{t}+c \\ &=e^{\tan ^{-1} x}+c \quad\quad\quad\quad\quad\left[\int e^{x} d x=e^{x}\right] \end{aligned}

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