Optimal. Leaf size=45 \[ \frac {7}{405} (2+3 x)^5-\frac {4}{27} (2+3 x)^6+\frac {65}{189} (2+3 x)^7-\frac {25}{324} (2+3 x)^8 \]
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Rubi [A]
time = 0.01, antiderivative size = 45, 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 = {78}
\begin {gather*} -\frac {25}{324} (3 x+2)^8+\frac {65}{189} (3 x+2)^7-\frac {4}{27} (3 x+2)^6+\frac {7}{405} (3 x+2)^5 \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {7}{27} (2+3 x)^4-\frac {8}{3} (2+3 x)^5+\frac {65}{9} (2+3 x)^6-\frac {50}{27} (2+3 x)^7\right ) \, dx\\ &=\frac {7}{405} (2+3 x)^5-\frac {4}{27} (2+3 x)^6+\frac {65}{189} (2+3 x)^7-\frac {25}{324} (2+3 x)^8\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 47, normalized size = 1.04 \begin {gather*} 144 x+528 x^2+\frac {2536 x^3}{3}+94 x^4-\frac {9039 x^5}{5}-2898 x^6-\frac {13635 x^7}{7}-\frac {2025 x^8}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 40, normalized size = 0.89
method | result | size |
gosper | \(-\frac {x \left (212625 x^{7}+818100 x^{6}+1217160 x^{5}+759276 x^{4}-39480 x^{3}-355040 x^{2}-221760 x -60480\right )}{420}\) | \(39\) |
default | \(-\frac {2025}{4} x^{8}-\frac {13635}{7} x^{7}-2898 x^{6}-\frac {9039}{5} x^{5}+94 x^{4}+\frac {2536}{3} x^{3}+528 x^{2}+144 x\) | \(40\) |
norman | \(-\frac {2025}{4} x^{8}-\frac {13635}{7} x^{7}-2898 x^{6}-\frac {9039}{5} x^{5}+94 x^{4}+\frac {2536}{3} x^{3}+528 x^{2}+144 x\) | \(40\) |
risch | \(-\frac {2025}{4} x^{8}-\frac {13635}{7} x^{7}-2898 x^{6}-\frac {9039}{5} x^{5}+94 x^{4}+\frac {2536}{3} x^{3}+528 x^{2}+144 x\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 39, normalized size = 0.87 \begin {gather*} -\frac {2025}{4} \, x^{8} - \frac {13635}{7} \, x^{7} - 2898 \, x^{6} - \frac {9039}{5} \, x^{5} + 94 \, x^{4} + \frac {2536}{3} \, x^{3} + 528 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.04, size = 39, normalized size = 0.87 \begin {gather*} -\frac {2025}{4} \, x^{8} - \frac {13635}{7} \, x^{7} - 2898 \, x^{6} - \frac {9039}{5} \, x^{5} + 94 \, x^{4} + \frac {2536}{3} \, x^{3} + 528 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 44, normalized size = 0.98 \begin {gather*} - \frac {2025 x^{8}}{4} - \frac {13635 x^{7}}{7} - 2898 x^{6} - \frac {9039 x^{5}}{5} + 94 x^{4} + \frac {2536 x^{3}}{3} + 528 x^{2} + 144 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.98, size = 39, normalized size = 0.87 \begin {gather*} -\frac {2025}{4} \, x^{8} - \frac {13635}{7} \, x^{7} - 2898 \, x^{6} - \frac {9039}{5} \, x^{5} + 94 \, x^{4} + \frac {2536}{3} \, x^{3} + 528 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 39, normalized size = 0.87 \begin {gather*} -\frac {2025\,x^8}{4}-\frac {13635\,x^7}{7}-2898\,x^6-\frac {9039\,x^5}{5}+94\,x^4+\frac {2536\,x^3}{3}+528\,x^2+144\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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