# How do I evaluate the integral #int7x^2 ln(x) dx#?

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To evaluate the integral ∫7x^2 ln(x) dx, you can use integration by parts. Let u = ln(x) and dv = 7x^2 dx. Then, differentiate u to find du and integrate dv to find v. After finding u, du, v, and dv, use the integration by parts formula:

∫u dv = uv - ∫v du

Then substitute the values of u, v, du, and dv into the formula and solve the integral.

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To evaluate the integral ∫7x^2 ln(x) dx, you can use integration by parts. Let u = ln(x) and dv = 7x^2 dx. Then, differentiate u to get du and integrate dv to get v. Once you have u, du, v, and dv, use the integration by parts formula:

∫u dv = uv - ∫v du

Substitute the values of u, dv, v, and du into the formula and integrate accordingly.

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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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