Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- Load more...
Rewrite the expression $\frac{8x^2+12x+12}{x^3-3x^2+3x-9}$ inside the integral in factored form
Learn how to solve problems step by step online.
$\int_{-3}^{4}\frac{8x^2+12x+12}{\left(x^{2}+3\right)\left(x-3\right)}dx$
Learn how to solve problems step by step online. Integrate the function (8x^2+12x+12)/(x^3-3x^23x+-9) from -3 to 4. Rewrite the expression \frac{8x^2+12x+12}{x^3-3x^2+3x-9} inside the integral in factored form. Rewrite the fraction \frac{8x^2+12x+12}{\left(x^{2}+3\right)\left(x-3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int_{-3}^{4}\left(\frac{-2x+6}{x^{2}+3}+\frac{10}{x-3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-3}^{4}\frac{-2x+6}{x^{2}+3}dx results in: \ln\left(\frac{3}{19}\right)-2\ln\left(\frac{1}{2}\right)+6\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{4}{\sqrt{3}}\right)-6\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{-3}{\sqrt{3}}\right).
