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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 52

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Answer: \tan x + \sec x + c

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

Given: \int \sec x\left ( \sec x+\tan x \right )dx\int \sec x\left ( \sec x+\tan x \right ) dx


\begin{aligned} &\int \sec ^{2} x+\sec x \tan x d x \\ &\int \sec ^{2} x d x+\int \sec x \cdot \tan x d x \\ &\tan x+\sec x+c\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\left[\because \int \sec ^{2} x d x=\tan x \text { and } \int \sec x \cdot \tan x d x=\sec x+c\right] \\ \end{aligned}

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