1. ## integration by substitution

integrate

dx/ x^4(1+x^2)^(1/2)

using the substitution x = 1/ (u^2-1)^(1/2)

and

x^2(1+x^2)^(1/2) using the substitution x = tan u

p.s.

does anyone know exactly how to write these equations and formulas "properly", with the integral sign and such? I have a program called mathematica but it is not compatible here on the forum.

2. Hello, mathshelpneeded!

I can get you started on the second one . . .

x²(1 + x²)^½ dx, .using the substitution: x = tanθ

We have: .x = tanθ . . dx = sec²θ·dθ
. . and the radical becomes: secθ

Substitute: .
tan²θ·secθ·sec²θ·dθ . = . sec³θ·tan²θ·dθ

This integral is particularly annoying to integrate.
. . It has an odd-powered secant and an even-powered tangent.
It requires integration by parts and some fancy algebra.