Optimal. Leaf size=35 \[ 18 x+\frac {15 x^2}{2}-\frac {136 x^3}{3}-\frac {137 x^4}{4}+52 x^5+50 x^6 \]
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Rubi [A]
time = 0.01, antiderivative size = 35, 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*} 50 x^6+52 x^5-\frac {137 x^4}{4}-\frac {136 x^3}{3}+\frac {15 x^2}{2}+18 x \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x) (3+5 x)^2 \, dx &=\int \left (18+15 x-136 x^2-137 x^3+260 x^4+300 x^5\right ) \, dx\\ &=18 x+\frac {15 x^2}{2}-\frac {136 x^3}{3}-\frac {137 x^4}{4}+52 x^5+50 x^6\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 35, normalized size = 1.00 \begin {gather*} 18 x+\frac {15 x^2}{2}-\frac {136 x^3}{3}-\frac {137 x^4}{4}+52 x^5+50 x^6 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 30, normalized size = 0.86
method | result | size |
gosper | \(\frac {x \left (600 x^{5}+624 x^{4}-411 x^{3}-544 x^{2}+90 x +216\right )}{12}\) | \(29\) |
default | \(18 x +\frac {15}{2} x^{2}-\frac {136}{3} x^{3}-\frac {137}{4} x^{4}+52 x^{5}+50 x^{6}\) | \(30\) |
norman | \(18 x +\frac {15}{2} x^{2}-\frac {136}{3} x^{3}-\frac {137}{4} x^{4}+52 x^{5}+50 x^{6}\) | \(30\) |
risch | \(18 x +\frac {15}{2} x^{2}-\frac {136}{3} x^{3}-\frac {137}{4} x^{4}+52 x^{5}+50 x^{6}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 29, normalized size = 0.83 \begin {gather*} 50 \, x^{6} + 52 \, x^{5} - \frac {137}{4} \, x^{4} - \frac {136}{3} \, x^{3} + \frac {15}{2} \, x^{2} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 29, normalized size = 0.83 \begin {gather*} 50 \, x^{6} + 52 \, x^{5} - \frac {137}{4} \, x^{4} - \frac {136}{3} \, x^{3} + \frac {15}{2} \, x^{2} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 32, normalized size = 0.91 \begin {gather*} 50 x^{6} + 52 x^{5} - \frac {137 x^{4}}{4} - \frac {136 x^{3}}{3} + \frac {15 x^{2}}{2} + 18 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.62, size = 29, normalized size = 0.83 \begin {gather*} 50 \, x^{6} + 52 \, x^{5} - \frac {137}{4} \, x^{4} - \frac {136}{3} \, x^{3} + \frac {15}{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 = 29, normalized size = 0.83 \begin {gather*} 50\,x^6+52\,x^5-\frac {137\,x^4}{4}-\frac {136\,x^3}{3}+\frac {15\,x^2}{2}+18\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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