Optimal. Leaf size=46 \[ -\frac {600 x^7}{7}-\frac {110 x^6}{3}+\frac {534 x^5}{5}+\frac {135 x^4}{4}-\frac {166 x^3}{3}-\frac {21 x^2}{2}+18 x \]
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Rubi [A] time = 0.02, antiderivative size = 46, 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} \[ -\frac {600 x^7}{7}-\frac {110 x^6}{3}+\frac {534 x^5}{5}+\frac {135 x^4}{4}-\frac {166 x^3}{3}-\frac {21 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x) (3+5 x)^2 \, dx &=\int \left (18-21 x-166 x^2+135 x^3+534 x^4-220 x^5-600 x^6\right ) \, dx\\ &=18 x-\frac {21 x^2}{2}-\frac {166 x^3}{3}+\frac {135 x^4}{4}+\frac {534 x^5}{5}-\frac {110 x^6}{3}-\frac {600 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 46, normalized size = 1.00 \[ -\frac {600 x^7}{7}-\frac {110 x^6}{3}+\frac {534 x^5}{5}+\frac {135 x^4}{4}-\frac {166 x^3}{3}-\frac {21 x^2}{2}+18 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 34, normalized size = 0.74 \[ -\frac {600}{7} x^{7} - \frac {110}{3} x^{6} + \frac {534}{5} x^{5} + \frac {135}{4} x^{4} - \frac {166}{3} x^{3} - \frac {21}{2} x^{2} + 18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.82, size = 34, normalized size = 0.74 \[ -\frac {600}{7} \, x^{7} - \frac {110}{3} \, x^{6} + \frac {534}{5} \, x^{5} + \frac {135}{4} \, x^{4} - \frac {166}{3} \, x^{3} - \frac {21}{2} \, x^{2} + 18 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.76 \[ -\frac {600}{7} x^{7}-\frac {110}{3} x^{6}+\frac {534}{5} x^{5}+\frac {135}{4} x^{4}-\frac {166}{3} x^{3}-\frac {21}{2} x^{2}+18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 34, normalized size = 0.74 \[ -\frac {600}{7} \, x^{7} - \frac {110}{3} \, x^{6} + \frac {534}{5} \, x^{5} + \frac {135}{4} \, x^{4} - \frac {166}{3} \, x^{3} - \frac {21}{2} \, x^{2} + 18 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 34, normalized size = 0.74 \[ -\frac {600\,x^7}{7}-\frac {110\,x^6}{3}+\frac {534\,x^5}{5}+\frac {135\,x^4}{4}-\frac {166\,x^3}{3}-\frac {21\,x^2}{2}+18\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 42, normalized size = 0.91 \[ - \frac {600 x^{7}}{7} - \frac {110 x^{6}}{3} + \frac {534 x^{5}}{5} + \frac {135 x^{4}}{4} - \frac {166 x^{3}}{3} - \frac {21 x^{2}}{2} + 18 x \]
Verification of antiderivative is not currently implemented for this CAS.
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