# How do I find the antiderivative of #f(x)=(5x^2) / (x^2 + 1)#?

Now you can integrate:

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To find the antiderivative of ( f(x) = \frac{5x^2}{x^2 + 1} ), you can use the method of partial fraction decomposition followed by integration. After decomposing ( f(x) ) into partial fractions, you can integrate each term separately. The antiderivative will be:

[ \int \frac{5x^2}{x^2 + 1} , dx = \int \left(5 - \frac{5}{x^2 + 1}\right) , dx ]

[ = 5x - 5\arctan(x) + C ]

Where ( C ) is the constant of integration.

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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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