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

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

Answers (1)

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 ]

=\frac{1}{3}u^{3}+c

=\frac{1}{3}\sec^{3}x+c

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