# How do you integrate #int 1/(x^2+2x+2)^2# by trigonometric substitution?

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To integrate ( \frac{1}{{(x^2 + 2x + 2)}^2} ) by trigonometric substitution, perform the following steps:

- Complete the square in the denominator: ( x^2 + 2x + 2 = (x + 1)^2 + 1 ).
- Substitute ( x + 1 = \tan(\theta) ) to express ( x ) in terms of ( \theta ).
- Find ( dx ) in terms of ( d\theta ).
- Rewrite the integrand in terms of ( \theta ).
- Integrate with respect to ( \theta ).
- Replace ( \theta ) with its inverse tangent expression.
- Simplify the expression.

The final result will be the integral of ( \frac{1}{{(x^2 + 2x + 2)}^2} ) using trigonometric substitution.

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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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