Final answer to the problem
$2x^{9}+\frac{51}{8}x^{8}-\frac{30}{7}x^{7}-\frac{35}{2}x^{6}+\frac{16}{5}x^{5}-\frac{57}{2}x^{4}-9x^{3}+\frac{131}{2}x^2-42x+C_0$
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Step-by-step Solution
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Find the integral
$\int\left(6x^5-7x^4-11x+6\right)\left(3x^3+12x^2+9x-7\right)dx$
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$\int\left(6x^5-7x^4-11x+6\right)\left(3x^3+12x^2+9x-7\right)dx$
Learn how to solve problems step by step online. Find the integral of f(x)=(6x^5-7x^4-11x+6)(3x^3+12x^29x+-7). Find the integral. Rewrite the integrand \left(6x^5-7x^4-11x+6\right)\left(3x^3+12x^2+9x-7\right) in expanded form. Expand the integral \int\left(18x^{8}+51x^{7}-30x^{6}-105x^{5}+16x^{4}-114x^3-27x^2+131x-42\right)dx into 9 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int18x^{8}dx results in: 2x^{9}.
Final answer to the problem
$2x^{9}+\frac{51}{8}x^{8}-\frac{30}{7}x^{7}-\frac{35}{2}x^{6}+\frac{16}{5}x^{5}-\frac{57}{2}x^{4}-9x^{3}+\frac{131}{2}x^2-42x+C_0$