# How do you find #int (2x)/((1-x)(1+x^2)) dx# using partial fractions?

Develop the integral in partial fractions:

So:

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

To find ∫(2x)/((1-x)(1+x^2)) dx using partial fractions, follow these steps:

- Decompose the fraction into partial fractions.
- Find the values of the unknown constants.
- Integrate each partial fraction separately.

The partial fraction decomposition of (2x)/((1-x)(1+x^2)) is:

(2x)/((1-x)(1+x^2)) = A/(1-x) + (Bx + C)/(1+x^2)

To find the values of A, B, and C, multiply both sides by the denominator:

2x = A(1+x^2) + (Bx + C)(1-x)

Then, equate coefficients of like terms:

For x^2 term: 0 = A + B For x term: 2 = -A + C For constant term: 0 = A - C

Solve this system of equations to find A, B, and C.

After finding the values of A, B, and C, integrate each partial fraction separately:

∫A/(1-x) dx + ∫(Bx + C)/(1+x^2) dx

The integral of A/(1-x) with respect to x is A * ln|1-x| + C1, where C1 is the constant of integration.

The integral of (Bx + C)/(1+x^2) with respect to x can be found using trigonometric substitution or other methods depending on your preference.

This process allows you to find the integral of (2x)/((1-x)(1+x^2)) dx using partial fractions.

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

- Are there functions that cannot be integrated using integration by parts?
- How do you find the integral of #sin(lnx) dx#?
- How do you use integration by parts to find #intxe^-x dx#?
- What is the antiderivative of #ln(x^3)/x#?
- How do you use partial fraction decomposition to decompose the fraction to integrate #2/(x^3-x^2)#?

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