Question

integral x(sqrt(1+x)) dx show me how to do with u substitution please

Answer 1

It's not real efficient to do this with u substitution. You wind up with the same thing you start off with. I'd just change the square root to a powered quantity and distribute.

Answer 2

can you show me how to do this then?

Answer 3

Yeah, let's just use u substitution anyway. With u substitution you want to rewrite the integral to an easier form to work with so try setting u=x+1.

Answer 4

i did that and it ends up so dx=du and x=u-1

Answer 5

Yes. So substitute those values back into the integral to get it in term of u, then distribute.

Answer 6

Then integrate with respect to u and when you're done, get the answer back in terms of x.

Answer 7

\[\int\limits_{}^{}\left( u-1 \right)\sqrt{u}du\] okay?

Answer 8

i dont know how to integrate that term

Answer 9

Yes. And you can rewrite the square root of u as u^(1/2). So then all you do is distribute that through (u-1).