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 = 0.0179223, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, 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*}
Mathematica [A] time = 0.0008616, size = 44, normalized size = 1. \[ -\frac{1350 x^7}{7}-\frac{1215 x^6}{2}-\frac{3366 x^5}{5}-\frac{769 x^4}{4}+\frac{638 x^3}{3}+210 x^2+72 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 35, normalized size = 0.8 \begin{align*} 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*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.23914, size = 46, normalized size = 1.05 \begin{align*} -\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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.30143, size = 108, normalized size = 2.45 \begin{align*} -\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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.060896, size = 41, normalized size = 0.93 \begin{align*} - \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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.90193, size = 46, normalized size = 1.05 \begin{align*} -\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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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