INTEGRAL of 1/(x^2+d^2)^1/2

Homework Statement

To find the INTEGRAL of 1/(x^2+d^2)^1/2 integrated with respect to dx.
d is a constant

I tried to write it as :

ln (x^2+ d^2)^1/2

but my book gives an answer of

ln { x + (x^2+ d^2)^1/2 }

i don't understand how. Can you plz explain it step by step. Clearly plz.

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lanedance
Homework Helper
how about starting with the subtitution x = d.sec(u)?

hunt_mat
Homework Helper
Even better, use the substitution:

$$x=d\sinh u$$

Last edited:
lanedance
Homework Helper
actually i meant x = d.tan(u), which makes more sense... but i'd still try huntmat's suggestion

lanedance
Homework Helper
also d is a bad constant to use when you're differentiating as you may get confused, something like a or s would be better