# How do you evaluate the integral #int xlnxdx#?

The 'integration by parts' method is required for this, and its formula must be understood.

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To evaluate the integral ∫xln(x)dx, we use integration by parts. Let u = ln(x) and dv = xdx. Then, du = (1/x)dx and v = (1/2)x^2.

Now, using the integration by parts formula: ∫u dv = uv - ∫v du,

we have: ∫xln(x)dx = (1/2)x^2ln(x) - ∫(1/2)x^2 * (1/x) dx.

Simplify the second integral: ∫(1/2)x dx.

Integrate to get: (1/4)x^2.

So, the final result is: (1/2)x^2ln(x) - (1/4)x^2 + 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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