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Expand the integral $\int\left(\frac{x^3}{x^4+8x^2+16}-2x^2+x-3\right)dx$ into $4$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int\frac{x^3}{x^4+8x^2+16}dx+\int-2x^2dx+\int xdx+\int-3dx$
Learn how to solve problems step by step online. Integrate int((x^3)/(x^4+8x^2+16)-2x^2x+-3)dx. Expand the integral \int\left(\frac{x^3}{x^4+8x^2+16}-2x^2+x-3\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x^3}{x^4+8x^2+16}dx results in: -\ln\left(\frac{2}{\sqrt{x^{2}+4}}\right)+\frac{2}{x^{2}+4}. The integral \int-2x^2dx results in: -\frac{2}{3}x^{3}. The integral \int xdx results in: \frac{1}{2}x^2.