Optimal. Leaf size=30 \[ -30 x^5-\frac {205 x^4}{4}-\frac {34 x^3}{3}+\frac {51 x^2}{2}+18 x \]
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Rubi [A] time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {77} \begin {gather*} -30 x^5-\frac {205 x^4}{4}-\frac {34 x^3}{3}+\frac {51 x^2}{2}+18 x \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x) (3+5 x)^2 \, dx &=\int \left (18+51 x-34 x^2-205 x^3-150 x^4\right ) \, dx\\ &=18 x+\frac {51 x^2}{2}-\frac {34 x^3}{3}-\frac {205 x^4}{4}-30 x^5\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} -30 x^5-\frac {205 x^4}{4}-\frac {34 x^3}{3}+\frac {51 x^2}{2}+18 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) (2+3 x) (3+5 x)^2 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.04, size = 24, normalized size = 0.80 \begin {gather*} -30 x^{5} - \frac {205}{4} x^{4} - \frac {34}{3} x^{3} + \frac {51}{2} x^{2} + 18 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 24, normalized size = 0.80 \begin {gather*} -30 \, x^{5} - \frac {205}{4} \, x^{4} - \frac {34}{3} \, x^{3} + \frac {51}{2} \, x^{2} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \begin {gather*} -30 x^{5}-\frac {205}{4} x^{4}-\frac {34}{3} x^{3}+\frac {51}{2} x^{2}+18 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 24, normalized size = 0.80 \begin {gather*} -30 \, x^{5} - \frac {205}{4} \, x^{4} - \frac {34}{3} \, x^{3} + \frac {51}{2} \, x^{2} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 24, normalized size = 0.80 \begin {gather*} -30\,x^5-\frac {205\,x^4}{4}-\frac {34\,x^3}{3}+\frac {51\,x^2}{2}+18\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 27, normalized size = 0.90 \begin {gather*} - 30 x^{5} - \frac {205 x^{4}}{4} - \frac {34 x^{3}}{3} + \frac {51 x^{2}}{2} + 18 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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