# How do you evaluate the integral of #(ln x)^2 dx#?

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bp has one great solution Method 1. There are other solutions:

Both of the solution presented below use Integration by Parts. I use the form:

Method 2

Integration by parts gives us:

Method 3

The parts formula gives us:

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

∫ u dv = uv - ∫ v du

Substitute the values of u, v, du, and dv into the formula and solve 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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