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

The answer is

Let's factorise,

Therefore,

So,

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I have found the following results with one substitution:

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To integrate ( \frac{x^2 + 2x}{x^2 + 2x + 1} ) using substitution, you can first factor the denominator to ( (x + 1)^2 ). Then, let ( u = x + 1 ). After that, express ( x ) and ( dx ) in terms of ( u ) and ( du ), respectively. Finally, substitute these expressions into the integral and simplify. The resulting integral will be easier to solve.

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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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