# Integration of (1/((x+(x^2+1)^(1/2))^3 at limit 0 to infinite ?

Evaluate:

Use now the trigonometric identity:

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To integrate the function (\frac{1}{(x+(x^2+1)^{1/2})^3}) from 0 to infinity, we can follow these steps:

- Make a substitution (u = x + \sqrt{x^2 + 1}).
- Compute (du).
- Express the integral in terms of (u).
- Integrate with respect to (u) from (u = 1) to (u = \infty).
- Substitute back the expression for (x) in terms of (u).
- Evaluate the limits.

If you need further clarification on any of these steps, feel free to ask!

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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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