Optimal. Leaf size=49 \[ -\frac {3375 x^8}{4}-\frac {22275 x^7}{7}-\frac {9255 x^6}{2}-\frac {13943 x^5}{5}+\frac {883 x^4}{4}+1338 x^3+810 x^2+216 x \]
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Rubi [A] time = 0.02, antiderivative size = 49, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {77} \[ -\frac {3375 x^8}{4}-\frac {22275 x^7}{7}-\frac {9255 x^6}{2}-\frac {13943 x^5}{5}+\frac {883 x^4}{4}+1338 x^3+810 x^2+216 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^3 (3+5 x)^3 \, dx &=\int \left (216+1620 x+4014 x^2+883 x^3-13943 x^4-27765 x^5-22275 x^6-6750 x^7\right ) \, dx\\ &=216 x+810 x^2+1338 x^3+\frac {883 x^4}{4}-\frac {13943 x^5}{5}-\frac {9255 x^6}{2}-\frac {22275 x^7}{7}-\frac {3375 x^8}{4}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 49, normalized size = 1.00 \[ -\frac {3375 x^8}{4}-\frac {22275 x^7}{7}-\frac {9255 x^6}{2}-\frac {13943 x^5}{5}+\frac {883 x^4}{4}+1338 x^3+810 x^2+216 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 39, normalized size = 0.80 \[ -\frac {3375}{4} x^{8} - \frac {22275}{7} x^{7} - \frac {9255}{2} x^{6} - \frac {13943}{5} x^{5} + \frac {883}{4} x^{4} + 1338 x^{3} + 810 x^{2} + 216 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.24, size = 39, normalized size = 0.80 \[ -\frac {3375}{4} \, x^{8} - \frac {22275}{7} \, x^{7} - \frac {9255}{2} \, x^{6} - \frac {13943}{5} \, x^{5} + \frac {883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.82 \[ -\frac {3375}{4} x^{8}-\frac {22275}{7} x^{7}-\frac {9255}{2} x^{6}-\frac {13943}{5} x^{5}+\frac {883}{4} x^{4}+1338 x^{3}+810 x^{2}+216 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 39, normalized size = 0.80 \[ -\frac {3375}{4} \, x^{8} - \frac {22275}{7} \, x^{7} - \frac {9255}{2} \, x^{6} - \frac {13943}{5} \, x^{5} + \frac {883}{4} \, x^{4} + 1338 \, x^{3} + 810 \, x^{2} + 216 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 39, normalized size = 0.80 \[ -\frac {3375\,x^8}{4}-\frac {22275\,x^7}{7}-\frac {9255\,x^6}{2}-\frac {13943\,x^5}{5}+\frac {883\,x^4}{4}+1338\,x^3+810\,x^2+216\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 46, normalized size = 0.94 \[ - \frac {3375 x^{8}}{4} - \frac {22275 x^{7}}{7} - \frac {9255 x^{6}}{2} - \frac {13943 x^{5}}{5} + \frac {883 x^{4}}{4} + 1338 x^{3} + 810 x^{2} + 216 x \]
Verification of antiderivative is not currently implemented for this CAS.
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