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Question: Answered & Verified by Expert
$\int \sec x \tan ^3 x d x=$
MathematicsIndefinite IntegrationJEE Main
Options:
  • A $\frac{1}{3} \sec ^3 x-\sec x+c$
  • B $\sec ^3 x-\sec x+c$
  • C $\frac{1}{3} \sec ^3 x+\sec x+c$
  • D None of these
Solution:
1914 Upvotes Verified Answer
The correct answer is: $\frac{1}{3} \sec ^3 x-\sec x+c$
$\begin{aligned} & \int \sec x \tan ^3 x d x=\int \sec x\left(\sec ^2 x-1\right) \tan x d x \\ & =\int \sec x \tan x \sec ^2 x d x-\int \sec x \tan x d x \\ & =\frac{\sec ^3 x}{3}-\sec x+c, \quad \text { (Putting } \sec x=t \text { in first part). }\end{aligned}$

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