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Expand the integral $\int_{-4}^{1}\left(\left(1-x^2\right)^2-\left(-3+x^2-2x\right)^2\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int_{-4}^{1}\left(1-x^2\right)^2dx+\int_{-4}^{1}-\left(-3+x^2-2x\right)^2dx$
Learn how to solve problems step by step online. Integrate the function (1-x^2)^2-(-3+x^2-2x)^2 from -4 to 1. Expand the integral \int_{-4}^{1}\left(\left(1-x^2\right)^2-\left(-3+x^2-2x\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(1-x^2\right)^2dx results in: \frac{500}{3}. The integral \int_{-4}^{1}-\left(-3+x^2-2x\right)^2dx results in: -\frac{1115}{3}. Gather the results of all integrals.