Optimal. Leaf size=34 \[ -\frac {10}{189} (3 x+2)^7+\frac {37}{162} (3 x+2)^6-\frac {7}{135} (3 x+2)^5 \]
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Rubi [A] time = 0.02, antiderivative size = 34, 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*} -\frac {10}{189} (3 x+2)^7+\frac {37}{162} (3 x+2)^6-\frac {7}{135} (3 x+2)^5 \end {gather*}
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^4 (3+5 x) \, dx &=\int \left (-\frac {7}{9} (2+3 x)^4+\frac {37}{9} (2+3 x)^5-\frac {10}{9} (2+3 x)^6\right ) \, dx\\ &=-\frac {7}{135} (2+3 x)^5+\frac {37}{162} (2+3 x)^6-\frac {10}{189} (2+3 x)^7\\ \end {align*}
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Mathematica [A] time = 0.00, size = 42, normalized size = 1.24 \begin {gather*} -\frac {810 x^7}{7}-\frac {747 x^6}{2}-\frac {2133 x^5}{5}-132 x^4+\frac {392 x^3}{3}+136 x^2+48 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)^4 (3+5 x) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.84, size = 34, normalized size = 1.00 \begin {gather*} -\frac {810}{7} x^{7} - \frac {747}{2} x^{6} - \frac {2133}{5} x^{5} - 132 x^{4} + \frac {392}{3} x^{3} + 136 x^{2} + 48 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.25, size = 34, normalized size = 1.00 \begin {gather*} -\frac {810}{7} \, x^{7} - \frac {747}{2} \, x^{6} - \frac {2133}{5} \, x^{5} - 132 \, x^{4} + \frac {392}{3} \, x^{3} + 136 \, x^{2} + 48 \, 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 = 1.03 \begin {gather*} -\frac {810}{7} x^{7}-\frac {747}{2} x^{6}-\frac {2133}{5} x^{5}-132 x^{4}+\frac {392}{3} x^{3}+136 x^{2}+48 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 34, normalized size = 1.00 \begin {gather*} -\frac {810}{7} \, x^{7} - \frac {747}{2} \, x^{6} - \frac {2133}{5} \, x^{5} - 132 \, x^{4} + \frac {392}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 34, normalized size = 1.00 \begin {gather*} -\frac {810\,x^7}{7}-\frac {747\,x^6}{2}-\frac {2133\,x^5}{5}-132\,x^4+\frac {392\,x^3}{3}+136\,x^2+48\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 39, normalized size = 1.15 \begin {gather*} - \frac {810 x^{7}}{7} - \frac {747 x^{6}}{2} - \frac {2133 x^{5}}{5} - 132 x^{4} + \frac {392 x^{3}}{3} + 136 x^{2} + 48 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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