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Simplify the expression
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$\int_{0}^{600}\left(1.732-1.52\times 10^{-3}x\right){\left(\left(4.17\times 10^{-6}x^2+\frac{-x^3}{2\cdot 600^3}\right)\right)}^2dx$
Learn how to solve limits to infinity problems step by step online. Integrate the function (1.732-1.52310^(-3.0)x)((3x^2)/(2600^2)+(-x^3)/(2600^3))^2 from 0 to 600. Simplify the expression. Rewrite the integrand \left(1.732-1.52\times 10^{-3}x\right){\left(\left(4.17\times 10^{-6}x^2+\frac{-x^3}{2\cdot 600^3}\right)\right)}^2 in expanded form. Expand the integral \int_{0}^{600}\left(1.732\cdot {\left(4.17\times 10^{-6}\right)}^{2}x^{4}+\frac{-7.22\times 10^{-6}x^{5}}{600^3}+\frac{1.732x^{6}}{4\cdot 600^{6}}-1.52\times 10^{-3}\cdot {\left(4.17\times 10^{-6}\right)}^{2}x^{5}+\frac{6.35\times 10^{-9}x^{6}}{600^3}+\frac{-3.81\times 10^{-4}x^{7}}{600^{6}}\right)dx into 6 integrals using the sum rule for integrals, to then solve each integral separately. Simplify the expression.
