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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 14

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Answer: \frac{1}{3}\sec^{3}x+c

Hint: You must know about the integration rule of trigonometric function.

Given: \int \tan x.\sec ^{3}x dx

Solution: let \sec x=u   differentiate both sides,  \left [ \frac{d}{dx}\sec x= \sec x.\tan x \right ]

          \sec x .\tan x dx= du

\therefore I= \int \sec^{2}x\left ( \sec x.\tan x \right )dx

=\int u^{2} du                                                   \left [ \int x^{n} dx= \frac{^{n+1}}{n+1} \right ]



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