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- Integrate using basic integrals
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Expand the integral $\int_{-4}^{1}\left(\left(x^2-1\right)^2-\left(-x^2+2x-3\right)^2\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int_{-4}^{1}\left(x^2-1\right)^2dx+\int_{-4}^{1}-\left(-x^2+2x-3\right)^2dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (x^2-1)^2-(-x^2+2x+-3)^2 from -4 to 1. Expand the integral \int_{-4}^{1}\left(\left(x^2-1\right)^2-\left(-x^2+2x-3\right)^2\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-4}^{1}\left(x^2-1\right)^2dx results in: \frac{500}{3}. The integral \int_{-4}^{1}-\left(-x^2+2x-3\right)^2dx results in: -\frac{226}{5}+\frac{{\left(-4\right)}^{5}}{5}-10\cdot \left(\frac{1}{3}+\frac{- {\left(-4\right)}^{3}}{3}\right)+4\cdot \left(\frac{1}{4}+\frac{- {\left(-4\right)}^{4}}{4}\right)+12\cdot \left(\frac{1}{2}-\frac{1}{2}\cdot {\left(-4\right)}^2\right). Gather the results of all integrals.