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What is the antiderivative of #(5/x)^2#?

Answer 1

Emilia Aguilar

#-25/x+C#

#(5/x)^2=5^2/x^2=25x^-2#

Recalling that #intx^adx=x^(a+1)/(a+1), a ne -1#,

#int25x^-2dx=25x^-1/-1=-25/x+C#

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Answer 2

Christopher Agresta

The antiderivative of (5/x)^2 is (25 ln|x|)/x + C, where C is the constant of integration.

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Answer 3

Isaiah Allen

The antiderivative of ( \left(\frac{5}{x}\right)^2 ) is ( -\frac{25}{x} + C ), where ( C ) is the constant of integration.

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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.