# what is the antiderivative of

1/(x^2-2x+2)?

does antiderivative mean find the derivative of the function or integrate it.

is-2(x^2-2x+2)^-2. These are part of the multiple choices.

antiderivative is the integral.

so would the answer be ln(x^2-2x+2).

also i need help with finding critical points of (x+2)^5*(x-3)^4

i got the derivative of that which is

[5(x+2)^4*(x-3)^4] + [4(x+3)^3*(x+2)^5] and i set it to zero and got a total of three zeros. i don't need to solve for them but are three zeros correct.

8 months ago

## To find the antiderivative of a function, you need to integrate it. In this case, the antiderivative of 1/(x^2-2x+2) can be found using a technique called partial fraction decomposition.

To solve this, you can start by factoring the denominator (x^2-2x+2). However, in this case, the denominator cannot be factored since it does not have any real roots. Therefore, you would need to use a different approach.

One way to approach this is by using a technique called completing the square. By completing the square, you can rewrite the denominator in a form that makes it easier to integrate. The completed square form of the denominator is (x-1)^2 + 1.

Now, you can rewrite 1/(x^2-2x+2) as 1/[(x-1)^2 + 1]. To integrate this, you can consider it as the derivative of the arctan function. The antiderivative of 1/[(x-1)^2 + 1] is arctan(x-1) + C, where C represents the constant of integration.

So, the correct antiderivative of 1/(x^2-2x+2) is arctan(x-1) + C.