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Rewrite the integrand $\sqrt{5x^4-x^2+10}\left(10x^3-x\right)$ in expanded form
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$\int\left(10\sqrt{5x^4-x^2+10}x^3-\sqrt{5x^4-x^2+10}x\right)dx$
Learn how to solve problems step by step online. Integrate int((5x^4-x^2+10)^(1/2)(10x^3-x))dx. Rewrite the integrand \sqrt{5x^4-x^2+10}\left(10x^3-x\right) in expanded form. Expand the integral \int\left(10\sqrt{5x^4-x^2+10}x^3-\sqrt{5x^4-x^2+10}x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int10\sqrt{5x^4-x^2+10}x^3dx results in: 5\int\sqrt{5u^{2}-u+10}udu. The integral \int-\sqrt{5x^4-x^2+10}xdx results in: -\frac{1}{2}\int\sqrt{5u^{2}-u+10}du.
