Optimal. Leaf size=44 \[ -\frac {1350 x^7}{7}-\frac {1215 x^6}{2}-\frac {3366 x^5}{5}-\frac {769 x^4}{4}+\frac {638 x^3}{3}+210 x^2+72 x \]
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Rubi [A] time = 0.02, antiderivative size = 44, 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} \[ -\frac {1350 x^7}{7}-\frac {1215 x^6}{2}-\frac {3366 x^5}{5}-\frac {769 x^4}{4}+\frac {638 x^3}{3}+210 x^2+72 x \]
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)^2 \, dx &=\int \left (72+420 x+638 x^2-769 x^3-3366 x^4-3645 x^5-1350 x^6\right ) \, dx\\ &=72 x+210 x^2+\frac {638 x^3}{3}-\frac {769 x^4}{4}-\frac {3366 x^5}{5}-\frac {1215 x^6}{2}-\frac {1350 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 44, normalized size = 1.00 \[ -\frac {1350 x^7}{7}-\frac {1215 x^6}{2}-\frac {3366 x^5}{5}-\frac {769 x^4}{4}+\frac {638 x^3}{3}+210 x^2+72 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 34, normalized size = 0.77 \[ -\frac {1350}{7} x^{7} - \frac {1215}{2} x^{6} - \frac {3366}{5} x^{5} - \frac {769}{4} x^{4} + \frac {638}{3} x^{3} + 210 x^{2} + 72 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 34, normalized size = 0.77 \[ -\frac {1350}{7} \, x^{7} - \frac {1215}{2} \, x^{6} - \frac {3366}{5} \, x^{5} - \frac {769}{4} \, x^{4} + \frac {638}{3} \, x^{3} + 210 \, x^{2} + 72 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.80 \[ -\frac {1350}{7} x^{7}-\frac {1215}{2} x^{6}-\frac {3366}{5} x^{5}-\frac {769}{4} x^{4}+\frac {638}{3} x^{3}+210 x^{2}+72 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 34, normalized size = 0.77 \[ -\frac {1350}{7} \, x^{7} - \frac {1215}{2} \, x^{6} - \frac {3366}{5} \, x^{5} - \frac {769}{4} \, x^{4} + \frac {638}{3} \, x^{3} + 210 \, x^{2} + 72 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.77 \[ -\frac {1350\,x^7}{7}-\frac {1215\,x^6}{2}-\frac {3366\,x^5}{5}-\frac {769\,x^4}{4}+\frac {638\,x^3}{3}+210\,x^2+72\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 41, normalized size = 0.93 \[ - \frac {1350 x^{7}}{7} - \frac {1215 x^{6}}{2} - \frac {3366 x^{5}}{5} - \frac {769 x^{4}}{4} + \frac {638 x^{3}}{3} + 210 x^{2} + 72 x \]
Verification of antiderivative is not currently implemented for this CAS.
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