Can anyone help me with this problem: Integrate ((x-1)/(sqrt x))dx. I realize that I can separate the integral with subtraction because that's one of the rules for integrals, but once I do that I have [(x*x^(-1/2))+x^(1/2)]dx . I don't know what to do with the first part of the quantity because of the multiplication.

Question

Can anyone help me with this problem: Integrate ((x-1)/(sqrt x))dx.  I realize that I can separate the integral with subtraction because that's one of the rules for integrals, but once I do that I have [(x*x^(-1/2))+x^(1/2)]dx . I don't know what to do with the first part of the quantity because of the multiplication.

anonymous · Answer

You can use substitution. Plug in $$u = \sqrt{x}$$ and $$du = \frac{1}{2\sqrt{x}}$$

Now, you can plug this back in to your integral. This next part may be a little confusing, but give it some thought. $$2\int\limits (u^{2} - 1) du$$

Solve that, and don't forget to plug in your u.

anonymous · Answer

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