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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 6

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Hint: You must know about the integration rule of tan and sec function

Given: \int \tan^{6}x \sec^{2 }xdx

Solution: Suppose \tan x=t  differentiate both sides,               \left [\frac{d}{dx}\tan x= sec^{2} x \right ]

\begin{aligned} &\operatorname{sec}^{2}x d x=d t \\ &=\int t^{6} d t \\ &=\frac{t^{7}}{7}+c \quad \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] \\ &=\frac{\tan ^{7} x}{7}+c \end{aligned}

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