Integration help

1. Dec 14, 2008

nonechelon

1. The problem statement, all variables and given/known data

integrate this

9x³/sqrt(1+x²)

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

but thats as far as i could go. its the 9x³ that confuses me on what i should do.

Last edited: Dec 14, 2008
2. Dec 14, 2008

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.

3. Dec 15, 2008

dextercioby

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

4. Dec 15, 2008

Dick

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

5. Dec 15, 2008

nonechelon

thanks guys for all the help really appreciate it