anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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Owlfred
  • Owlfred
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anonymous
  • anonymous
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
anonymous
  • anonymous
you can check by differentiating and see why it is correct by the chain rule. the u-sub is just the chain rule backwards

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anonymous
  • anonymous
ah, thankyou very much

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