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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 8

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 8

Answers (1)

Answer: e^{x}\sec x+c

Hint: You must know about the integral values of exponential function and trignometric function.

Given: \int e^{x}\sec x\left ( 1+\tan x \right )dx

Solution:

\int e^{x}\sec x\left ( 1+\tan x \right )dx

= \int e^{x}\left (\sec x+\sec x\tan x \right )dx
Lete^{x} \sec x=t  and differentiate both sides, by using \left [ \frac{d}{dx} uv=u\frac{d}{dx}v+v\frac{d}{dx}u \right ]

\begin{aligned} &\left(e^{x} \sec x(1+t \operatorname{an} x)\right) d x=d t \\ &\mathrm{I}=\int d t \\ &=\mathrm{t}+\mathrm{c}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\left[\int x^{n} d x=\frac{x^{n+1}}{n+1}\right] \\ &=\mathrm{e}^{x} \sec x+c \quad\left[\mathrm{t}=\mathrm{e}^{x} \sec x\right] \end{aligned}

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