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Expert: - 7/26/2006


Question
How do I integrate

integral dx/(x+x^.5)?

thanks

Answer
We want S 1/(x+x^.5) dx

Let u = x^.5
Then du/dx = .5x^-.5
and dx = 2x^.5 du

make this substitution into the integral and get

S 1/(x+x^.5) 2x^.5 du =

S 2/(x^.5 + 1) du =

S 2/(u + 1) du =

2ln(u + 1)

substitute x^.5 back in for u and get the answer ,

2ln(x^.5 + 1) + C

You can check this by taking the derivative.
good luck!

Calculus

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