# What is #int (-2x^3-x^2+x+2 ) / (2x^2- x +3 )#?

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

To integrate ( \frac{-2x^3 - x^2 + x + 2}{2x^2 - x + 3} ), we can perform polynomial long division or use partial fraction decomposition.

Using polynomial long division, divide ( -2x^3 - x^2 + x + 2 ) by ( 2x^2 - x + 3 ), which yields a quotient and a remainder.

Once the division is done, the integral will be expressed as the integral of the quotient plus the integral of the remainder over the divisor.

Alternatively, using partial fraction decomposition, we express the rational function ( \frac{-2x^3 - x^2 + x + 2}{2x^2 - x + 3} ) as the sum of simpler fractions.

We start by factoring the denominator ( 2x^2 - x + 3 ) if possible. If not, we can use the quadratic formula.

Then, we express the rational function as:

[ \frac{-2x^3 - x^2 + x + 2}{2x^2 - x + 3} = \frac{Ax + B}{2x^2 - x + 3} ]

We then solve for constants ( A ) and ( B ) by equating coefficients and find their values.

After decomposing the rational function into partial fractions, we integrate each term separately.

This process will yield the integral of the original rational function.

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 #cos^3 (x)dx#?
- What is the net area between #f(x) = x^2-sqrt(x+1) # and the x-axis over #x in [1, 7 ]#?
- How do you evaluate the definite integral by the limit definition given #int xdx# from [-2,3]?
- How do you calculate the derivative of #intsqrt((x^3-2x+6) )dx# from #[x^2,-2]#?
- How do you find the antiderivative of #Cos(2x)Sin(x)dx#?

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