# What is the antiderivative of #ln(x)^2#?

So essentially we are looking for one function that simplifies when it is differentiated, and one that simplifies when integrated (or at least is integrable).

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The antiderivative of ln(x)^2 is ∫ln(x)^2 dx = x*ln(x)^2 - 2∫ln(x) dx.

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The antiderivative of ( \ln(x)^2 ) is ( x \ln(x)^2 - 2\int \ln(x) , dx ).

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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.

- What is the antiderivative of #cos(x^2)#?
- How do you find the indefinite integral of #int x^2/(3-x^2)#?
- How do you evaluate the integral #int 1/(x-2)^(2/3)dx# from 1 to 4?
- How do you find the indefinite integral of #int (x^2-3x^2+5)/(x-3)#?
- How do you find the derivative of #g(x) = int 9*sqrt(1+t^8)dt# from 7 to #x^2#?

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