# How do you find #int (2x-5)/(x^2+2x+2)#?

The answer is

Let's rewrite

Therefore, the integral is

So, we have 2 integrals

Let's do the first one,

For the second integral,

Finally, we have

By signing up, you agree to our Terms of Service and Privacy Policy

To find the integral of (\frac{{2x - 5}}{{x^2 + 2x + 2}}), you can use partial fraction decomposition followed by integration. After decomposition, the expression becomes (\frac{{Ax + B}}{{x^2 + 2x + 2}}). Solving for (A) and (B) by equating coefficients, you get (A = 1) and (B = -3). Then, you integrate each term separately. The integral of (\frac{1}{{x^2 + 2x + 2}}) can be evaluated using trigonometric substitution. After integrating, you'll arrive at the final answer.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- How do you find the integral of #dx/sqrt(x^2-4)#?
- How do you integrate #int 1/sqrt(4x+8sqrtx+12) # using trigonometric substitution?
- How do you integrate #int 1/sqrt(9x^2-6x+5) # using trigonometric substitution?
- How do you integrate #ln(5x+3)#?
- How do you integrate #(sec2x) / (tan2x) dx# using substitution?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7