How do you integrate $int x^3/sqrt(x^2+25) dx$ using trigonometric substitution?

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Answer 1 · 2016-01-13T18:42:39

I'll start you off.....
Consider the following right triangle:

enter image source here

Find the following:
$1)tan(theta)$
$2)sec(theta)$
$3)dx/(d theta)$
$4)x^3$
$5)sqrt(x^2+25)$

You will then systematically replace all x terms (rectangular) with
$theta$ terms (trigonometric).

It's your turn now to get your hands dirty and fill in all algebraic details.

How do you integrate int x^3/sqrt(x^2+25) dxint x^3/sqrt(x^2+25) dx using trigonometric substitution?