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Write a Value of ∫ Tan 6 X Sec 2 X D X - Mathematics

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Question

Write a value of

\[\int \tan^6 x \sec^2 x \text{ dx }\] .
Sum
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Solution

Let I= \[\int\] tan6 x . sec2 x dx

Let tan x = t
sec2 x dx = dt
\[\therefore I =\]\[\int\] t6 . dt

\[= \frac{t^7}{7} + C\]
\[ = \frac{\tan^7 x}{7} + C \left( \because t = \tan x \right)\]

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Chapter 19: Indefinite Integrals - Very Short Answers [Page 197]

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RD Sharma Mathematics [English] Class 12
Chapter 19 Indefinite Integrals
Very Short Answers | Q 6 | Page 197

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