# How do you integrate #(x)/(x+10) dx#?

You could use two ways - pure algebra or partial fractions - either of which give you

Algebraic Methodology

Approach Using Partial Fractions

Alternatively, we can go about things a little differently if we'd like to practice with partial fractions or if the teacher is making us use this approach.

If you weren't required to use the partial fractions method, I wouldn't recommend it.

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To integrate (x)/(x+10) dx, you can use the method of partial fractions. After decomposition, the integral becomes the sum of two simpler integrals:

∫(x)/(x+10) dx = ∫(10/(x+10) - 10/(x+10)^2) dx

Integrate each term separately:

= 10 ln|x+10| - 10/(x+10) + C

So, the integral of (x)/(x+10) dx is 10 ln|x+10| - 10/(x+10) + C, where C is the constant of integration.

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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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