# How do you test the improper integral #int (x(1+x^2)^-2)dx# from #[0,oo)# and evaluate if possible?

Evaluate first the indefinite integral:

Now we have:

So the indefinite integral is convergent and we have:

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To test the improper integral ∫(x(1+x^2)^-2)dx from 0 to infinity and evaluate if possible, you can follow these steps:

- Determine the convergence of the integral by analyzing its behavior as x approaches infinity.
- Find any singular points within the interval of integration.
- Apply appropriate techniques, such as integration by substitution or partial fractions, if necessary.
- If the integral converges, evaluate it using the fundamental theorem of calculus or other applicable methods.

For this specific integral, you can follow these steps to evaluate it.

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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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- How to find the sum of this series?

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