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May 28, 2015

Homework Help: calculus

Posted by mathstudent on Monday, December 31, 2007 at 11:54am.

Calculate definite integral of
dx/(x^4 * sqrt(x^2 + 3))
Over (1,3)

I start with the substitution x = sqrt(3)*tan t

so:
sqrt(x^2 + 3) = sqrt(3) * sec t
dx = sqrt(3) * sec^2 t dt
x^4 = 9 * tan^4 t

The integral simplifies to:
= dt/(tan^3 t * sin t)

How do I solve that?

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