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Rewrite the integrand $x^5\left(3-x^2\right)^7$ in expanded form
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$\int\left(2187x^5-5103x^{7}+5103x^{9}-2835x^{11}+945x^{13}-189x^{15}+21x^{17}-x^{19}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(x^5(3-x^2)^7)dx. Rewrite the integrand x^5\left(3-x^2\right)^7 in expanded form. Expand the integral \int\left(2187x^5-5103x^{7}+5103x^{9}-2835x^{11}+945x^{13}-189x^{15}+21x^{17}-x^{19}\right)dx into 8 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2187x^5dx results in: \frac{729}{2}x^{6}. The integral \int-5103x^{7}dx results in: -\frac{5103}{8}x^{8}.