# How do I find the integral #int(5x^2+3x-2)/(x^3+2x^2)dx# ?

Let us look at some details.

by Partial Fraction Decomposition (details not included),

by Log Rule and Power Rule,

I hope that this was helpful.

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

To find the integral ∫(5x^2 + 3x - 2)/(x^3 + 2x^2) dx, you can use partial fraction decomposition. First, factor the denominator x^3 + 2x^2 as x^2(x + 2). Then, express the fraction as the sum of two fractions with undetermined coefficients: A/x + B/x^2 + C/(x + 2). Solve for A, B, and C by equating coefficients. Once you have A, B, and C, integrate each term separately, and then sum them up. The result will be the integral of the original expression.

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 antiderivative of #int 1/(x^2(1+x^2)) dx#?
- How do I evaluate #int(t +5) sin (t+5) dt#?
- How do you integrate #int 1/sqrt(x^2+4)# by trigonometric substitution?
- How do you integrate #int (1-x^2)/((x+1)(x-5)(x+2)) # using partial fractions?
- How do you find the antiderivative of #int sqrt(x^2-1) dx#?

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