Question

Hi I do not understand this integration solution.

The integral of (2v+1)/(v+v^2).dv=ln(v+v^2).

What happens with the 2v+1, where does it go?

Answer 1

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Answer 2

u-substitution

let u = v+v^2
du = (2v+1)dv
so the integral becomes 1/u du which is the ln(u) + C
sub back in to get the answer ln(v+v^2) + C

Answer 3

you can check by differentiating and see why it is correct by the chain rule. the u-sub is just the chain rule backwards

Answer 4

ah, thankyou very much