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

Answer 1

It is #int (lnx)^2dx= x*[(lnx)^2-2*lnx+2]+c#

The antiderivative is using integration by parts

#int (lnx)^2dx=int x'(lnx)^2dx=x*(lnx)^2-int x[(lnx)^2]'dx= x*(lnx)^2-int x2lnx1/xdx= x(lnx)^2-2int lnxdx= x(lnx)^2-2*[xlnx-int x1/xdx]= x*(lnx)^2-2xlnx+2x+c= x[(lnx)^2-2*lnx+2]+c#

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Answer 2

Emily Ammerman

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

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Answer 3

Ezra Adams

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

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Answer from HIX Tutor

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.