How Do You Integrate 9x³/sqrt(1+x²) with a Trigonometric Substitution?

[nonechelon]

Homework Statement

integrate this

9x³/sqrt(1+x²)

I know I am suppose to substitute using: x = tan x
dx = sec²x

but that's as far as i could go. its the 9x³ that confuses me on what i should do.
thank you for your help in advance.

 

[Tedjn]

You should not be substituting x = tan x. You should be substituting x = tan u. Then, dx = sec²u du. So substitute tan u everywhere there is a x, and sec²u du for dx to get a complete integral in u.

 

[dextercioby]

$$x= \sinh u$$ as a substitution should do the trick.

 

[Dick]

$$x= \sinh u$$ as a substitution should do the trick.

You don't need trig at all. u=1+x^2 will work fine. Try it.

 

[nonechelon]

thanks guys for all the help really appreciate it