Final answer to the problem
$\left(x+\frac{5}{6}\right)^{3}+\frac{131}{12}x+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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1
Rewrite the expression $3x^2-8x+13\left(x+1\right)$ inside the integral in factored form
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$\int\left(3\left(x+\frac{5}{6}\right)^2+\frac{131}{12}\right)dx$
Learn how to solve problems step by step online. Integrate int(3x^2-8x13(x+1))dx. Rewrite the expression 3x^2-8x+13\left(x+1\right) inside the integral in factored form. Expand the integral \int\left(3\left(x+\frac{5}{6}\right)^2+\frac{131}{12}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int3\left(x+\frac{5}{6}\right)^2dx results in: \left(x+\frac{5}{6}\right)^{3}. The integral \int\frac{131}{12}dx results in: \frac{131}{12}x.
Final answer to the problem
$\left(x+\frac{5}{6}\right)^{3}+\frac{131}{12}x+C_0$
