Integral of sec^4x - Solve with U-Substitution

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SUMMARY

The integral of secant raised to the fourth power, ∫sec^4x, can be effectively solved using u-substitution. The discussion emphasizes rewriting the integral as ∫sec^2x(1 + tan^2x)dx to facilitate the substitution. This approach leverages the identity sec^2x = 1 + tan^2x, allowing for a straightforward integration process. The solution highlights the importance of recognizing trigonometric identities in calculus.

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  • Learn about trigonometric identities, specifically secant and tangent
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Homework Statement



The ∫sec4x

Homework Equations





The Attempt at a Solution



Im not entirely sure how to do this. At first I was thinking u sub but then there's nothing for u'.
 
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What trig identities do you know involving se(x)?
 
ibaforsale said:

Homework Statement



The ∫sec4x

Homework Equations


The Attempt at a Solution



Im not entirely sure how to do this. At first I was thinking u sub but then there's nothing for u'.

Try writing it as$$
\int \sec^2x(1+\tan^2 x)~dx$$and look for a ##u## substitution.
 

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