How do you integrate $(5x)/ (x-2)^(1/2) dx$ ?

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Answer 1 · 2015-04-11T15:04:20

$f(x)=5intx/(x-2)^(1/2)dx$

Let's $u = x-2$

$du = 1$

$x = u +2$

Now we have : $=5int(u+2)/u^(1/2) du$

$=5intsqrt(u)du+10int1/sqrt(u)du$

$=[10/3sqrt(u^3)]+20[sqrt(u)]+C$

Substitute back

$10/3(x-2)^(3/2)+20(x-2)^(1/2)+C$

How do you integrate (5x)/ (x-2)^(1/2) dx(5x)/ (x-2)^(1/2) dx?