there is no numerator... now i'm confused. i know i use the trig sub is x=a tan theta
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sqrt(x^2+2x)=sqrt(x^2+2x+1-1)=sqrt((x+1)^2-1) sub: t=x+1 sqrt(t^2-1) sub: t=sec(k) . . .
ok so I get sqrt(sec^2(k)-1)d theta t=sec(k) so dt is the derivative of sec?
Hyperbolic substitution is easier in this case than trigonometric... . Now let so that and the integral becomes .
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