Struggling with a Deceptively Difficult Integral

Thread starter imranq
Start date Sep 11, 2008
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Integral

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The integral ∫(sec^4{x}tan^4{x}) dx from 0 to π/4 is initially perceived as simple but proves challenging. The key to solving it lies in the substitution u = tan(x), which simplifies the expression. After realizing this substitution, the problem becomes manageable. The discussion highlights the importance of recognizing the right approach to tackle seemingly difficult integrals. Ultimately, the integral can be solved effectively with the correct substitution.

Sep 11, 2008

imranq

Homework Statement

It looks deceptively easy, but I can't seem to get it...
\int^{\frac{\pi}{4}}_{0}{\\sec^4{x}\tan^4{x}}\,dx

Homework Equations

\sec^2{x} = \tan^2{x} +1

The Attempt at a Solution

I've tried, but they all end up as trigonometric polynomials

Last edited: Sep 11, 2008

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Sep 11, 2008

Dick

Science Advisor

Homework Helper

It IS easy. Substitute u=tan(x).

Sep 11, 2008

imranq

ah shoot! Thanks, now I got it

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