# How do you integrate #(xdx)/(x^2+2)^3# which has the upper and lower limits, 2 and 1 ?

The indefinite integral is equal to

First. compute the indefinite intregral:

Power rule:

That's the result. Hope this helped!

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To integrate the function (\frac{xdx}{(x^2+2)^3}) with limits from 1 to 2, you can use a trigonometric substitution. Let (x = \sqrt{2}\tan(\theta)). Then (dx = \sqrt{2}\sec^2(\theta) d\theta). Substitute these expressions into the integral and simplify. After integration, apply the limits of integration from 1 to 2.

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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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