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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.

MIT 18.01 Single Variable Calculus (OCW)
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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.
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Thank you for your help.

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You can also use the substitution U = X. Its probably easier if you are not very comfortable with differentiating powers.

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