Final answer to the problem
$\frac{500}{3}x^{12}+424x^{10}+435x^{8}+\frac{680}{3}x^{6}+\frac{245}{4}x^{4}-\frac{1200}{11}x^{11}-\frac{2416}{9}x^{9}-\frac{1832}{7}x^{7}-\frac{624}{5}x^{5}-\frac{83}{3}x^{3}+\frac{15}{2}x^2-x+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\left(5x-1\right)^3\left(2x^2+1\right)^4dx$
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$\int\left(5x-1\right)^3\left(2x^2+1\right)^4dx$
Learn how to solve problems step by step online. Find the integral of (5x-1)^3(2x^2+1)^4. Find the integral. Rewrite the integrand \left(5x-1\right)^3\left(2x^2+1\right)^4 in expanded form. Expand the integral \int\left(2000x^{11}+4240x^{9}+3480x^{7}+1360x^{5}+245x^{3}-1200x^{10}-2416x^{8}-1832x^{6}-624x^{4}-83x^2+15x-1\right)dx into 12 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2000x^{11}dx results in: \frac{500}{3}x^{12}.
Final answer to the problem
$\frac{500}{3}x^{12}+424x^{10}+435x^{8}+\frac{680}{3}x^{6}+\frac{245}{4}x^{4}-\frac{1200}{11}x^{11}-\frac{2416}{9}x^{9}-\frac{1832}{7}x^{7}-\frac{624}{5}x^{5}-\frac{83}{3}x^{3}+\frac{15}{2}x^2-x+C_0$