Optimal. Leaf size=40 \[ -\frac {360 x^7}{7}-26 x^6+\frac {326 x^5}{5}+\frac {99 x^4}{4}-35 x^3-8 x^2+12 x \]
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Rubi [A] time = 0.02, antiderivative size = 40, 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} \begin {gather*} -\frac {360 x^7}{7}-26 x^6+\frac {326 x^5}{5}+\frac {99 x^4}{4}-35 x^3-8 x^2+12 x \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx &=\int \left (12-16 x-105 x^2+99 x^3+326 x^4-156 x^5-360 x^6\right ) \, dx\\ &=12 x-8 x^2-35 x^3+\frac {99 x^4}{4}+\frac {326 x^5}{5}-26 x^6-\frac {360 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 40, normalized size = 1.00 \begin {gather*} -\frac {360 x^7}{7}-26 x^6+\frac {326 x^5}{5}+\frac {99 x^4}{4}-35 x^3-8 x^2+12 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^3 (2+3 x)^2 (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.92, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360}{7} x^{7} - 26 x^{6} + \frac {326}{5} x^{5} + \frac {99}{4} x^{4} - 35 x^{3} - 8 x^{2} + 12 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.96, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360}{7} \, x^{7} - 26 \, x^{6} + \frac {326}{5} \, x^{5} + \frac {99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.88 \begin {gather*} -\frac {360}{7} x^{7}-26 x^{6}+\frac {326}{5} x^{5}+\frac {99}{4} x^{4}-35 x^{3}-8 x^{2}+12 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360}{7} \, x^{7} - 26 \, x^{6} + \frac {326}{5} \, x^{5} + \frac {99}{4} \, x^{4} - 35 \, x^{3} - 8 \, x^{2} + 12 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.85 \begin {gather*} -\frac {360\,x^7}{7}-26\,x^6+\frac {326\,x^5}{5}+\frac {99\,x^4}{4}-35\,x^3-8\,x^2+12\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 37, normalized size = 0.92 \begin {gather*} - \frac {360 x^{7}}{7} - 26 x^{6} + \frac {326 x^{5}}{5} + \frac {99 x^{4}}{4} - 35 x^{3} - 8 x^{2} + 12 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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