Final answer to the problem
$-\frac{5}{2}x^2+\frac{x^{3}}{12}+\frac{x^{3}}{3}+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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1
Solve the product $-\left(-x^2+4x\right)$
$\int\left(\frac{-x^2+4x}{-4}+x^2-4x\right)dx$
Learn how to solve integrals of polynomial functions problems step by step online.
$\int\left(\frac{-x^2+4x}{-4}+x^2-4x\right)dx$
Learn how to solve integrals of polynomial functions problems step by step online. Integrate int((-x^2+4x)/-4-(-x^2+4x))dx. Solve the product -\left(-x^2+4x\right). Expand the integral \int\left(\frac{-x^2+4x}{-4}+x^2-4x\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-x^2+4x}{-4}dx results in: \frac{x^{3}}{12}-\frac{1}{2}x^2. The integral \int x^2dx results in: \frac{x^{3}}{3}.
Final answer to the problem
$-\frac{5}{2}x^2+\frac{x^{3}}{12}+\frac{x^{3}}{3}+C_0$
