Question

I am trying to integrate (3x)(1+(x^2))^(1/2). Using integration by parts, I get u as 3x, du as 3 dx and dv comes as (1+(x^2)). To find v, I integrate dv and v comes out to be (1+(x^2))^(3/2) divided by 3x. I use the formula for integration by parts and get the answer. But it is not the correct answer. Why? http://www.wolframalpha.com/input/?i=Integrate+%283x%29%28%281%2Bx%5E%282%29%29%5E%281%2F2%29

Answer 1

Its just a simple substitution. Let w=1+x^2, dw=2xdx, 3/2 dw = 3x dx
Now you have \[ \int\limits_{}^{} (3/2) w ^{1/2} dw\]
just a simple power rule. then remember to replace w with 1+x^2.