# How do you integrate #int x^(1/2)*ln(x) # using integration by parts?

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To integrate ( \int x^{1/2} \cdot \ln(x) ) using integration by parts, you'll want to choose ( u = \ln(x) ) and ( dv = x^{1/2} , dx ). Then, differentiate ( u ) to find ( du ) and integrate ( dv ) to find ( v ). Apply the integration by parts formula ( \int u , dv = uv - \int v , du ). Finally, substitute the values back into the formula to find the integral.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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