Hi guys I'm trying to work through some problems getting ready for an exam and I came across this problem that doesn't make sense to me...

Consider $\displaystyle \displaystyle \int x(1+x^2)dx$

If I integrate this I get $\displaystyle 1/4(x^4) + 1/2(x^2)$

It says if we substitute x = sinh(u) we get $\displaystyle \displaystyle \int sinh(u)cosh^3(u)du$

Where on earth does that cosh^3 come from? I know that $\displaystyle 1+sinh^2(u)$ gives us $\displaystyle cosh^3(u)du.$

Also if I integrate this I get $\displaystyle \displaystyle \int sinh(u)cosh^3(u)du$ I get $\displaystyle x^4/4 + 2x^2/4 + 1/4$ . Why are they not equal?

Thoughts appreciated?