# What is the antiderivative of #ln(x)/sqrtx #?

For the given function, finding the antiderivative is equivalent to finding the indefinite integral. We will proceed by applying Integration by Parts.

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The antiderivative of ( \frac{\ln(x)}{\sqrt{x}} ) is given by:

[ \int \frac{\ln(x)}{\sqrt{x}} , dx = 2 \sqrt{x} \ln(x) - 4 \sqrt{x} + C ]

where ( C ) is the constant of integration.

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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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