Question

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

Answer 1

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

Explanation:

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.