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How do you find the indefinite integral of #int (x^2-4)/x#?

Answer 1

Paisley Johnson

#=1/2x^2-4ln|x|+C#

#int(x^2-4)/xdx# #=intx-4/xdx# #=1/2x^2-4ln|x|+C#

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Answer 2

Ezra Adams

To find the indefinite integral of ∫(x^2 - 4)/x, first, we rewrite the integrand as ∫(x - 4/x)dx. Then, we split the integral into two separate integrals: ∫x dx - ∫(4/x) dx. Integrating each term separately, we get (1/2)x^2 - 4ln(|x|) + C, where C is the constant of integration. Therefore, the indefinite integral of (x^2 - 4)/x is (1/2)x^2 - 4ln(|x|) + C.

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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.