# How do you integrate #int (5x²-2x-1)/( (x+1)(x²+1))# using partial fractions?

which turns into

Providing the framework with:

This provides the partial fraction breakdown for

Thus, we are now looking for

The initial integral is straightforward:

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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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