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antiderivative of fraction looking equation?

How would one tackle such a problem? Antiderivative of:

((√x)-4)÷((√x)-2)

Divide and rewrite as $1-\frac{2}{\sqrt{x}-2}$

$\int dx-2\int\frac{1}{\sqrt{x}-2}dx$

For the right one, let $u=\sqrt{x}-2, \;\ x=(u+2)^{2}, \;\ dx=2(u+2)du$

Hi, I've done what you've suggested and got:

x-2(x-4)log(√x-2)+C is this correct? I don't know if I applied it correctly, or do I apply the 2(u+2) to the right hand side as well as that is also?

Quote:

Originally Posted by galactus

Divide and rewrite as $1-\frac{2}{\sqrt{x}-2}$

$\int dx-2\int\frac{1}{\sqrt{x}-2}dx$

For the right one, let $u=\sqrt{x}-2, \;\ x=(u+2)^{2}, \;\ dx=2(u+2)du$

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