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How do you integrate #int 1/(x^(3/2) + x^(1/2)) dx#?

1 Answer

Sep 29, 2016

#2arc tansqrtx+C.#

Explanation:

Let #I=int1/(x^(3/2)+x^(1/2))dx=int1/{sqrtx(x+1)}dx#.

We take subst. #sqrtx=t, or, x=t^2 rArr dx=2tdt.#

#:. I=int1/(t(t^2+1))2tdt=2int1/(t^2+1)dt=2arc tant#

Hence, #I=2arc tansqrtx+C,# as Respected Eric Sia has derived!

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