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Evaluate: int(2x+1)/(sqrt(x^2)+2x-1)dx...

Evaluate: `int(2x+1)/(sqrt(x^2)+2x-1)dx`

Text Solution

Verified by Experts

I=`int(2x+1)/(sqrt(x^2+2x-1)dx`
Let `x^2+2x-1=t`
`2x+2=dt/dx`
I=`int(2x+2-1)/(sqrt(x^2+2x-1)dx`
I=`int(2x+2)/(sqrt(x^2+2x-1))dx-int(1)/(sqrt(x^2+2x-1)dx`
=`int dt/sqrt(t)-int dx/((x+1)^2-(sqrt(2))^2)`
=`2sqrt(t)-log|x+sqrt((x+1)^2-(sqrt(2))^2)|`
=`2sqrt(x^2+2x-1)-log|x+sqrt((x+1)^2-(sqrt(2))^2)|`
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