Optimal. Leaf size=34 \[ \frac {11}{500} (3+5 x)^4+\frac {31}{625} (3+5 x)^5-\frac {1}{125} (3+5 x)^6 \]
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Rubi [A]
time = 0.01, 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 = {78}
\begin {gather*} -\frac {1}{125} (5 x+3)^6+\frac {31}{625} (5 x+3)^5+\frac {11}{500} (5 x+3)^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x) (3+5 x)^3 \, dx &=\int \left (\frac {11}{25} (3+5 x)^3+\frac {31}{25} (3+5 x)^4-\frac {6}{25} (3+5 x)^5\right ) \, dx\\ &=\frac {11}{500} (3+5 x)^4+\frac {31}{625} (3+5 x)^5-\frac {1}{125} (3+5 x)^6\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 33, normalized size = 0.97 \begin {gather*} 54 x+\frac {243 x^2}{2}+51 x^3-\frac {785 x^4}{4}-295 x^5-125 x^6 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 30, normalized size = 0.88
method | result | size |
gosper | \(-\frac {x \left (500 x^{5}+1180 x^{4}+785 x^{3}-204 x^{2}-486 x -216\right )}{4}\) | \(29\) |
default | \(-125 x^{6}-295 x^{5}-\frac {785}{4} x^{4}+51 x^{3}+\frac {243}{2} x^{2}+54 x\) | \(30\) |
norman | \(-125 x^{6}-295 x^{5}-\frac {785}{4} x^{4}+51 x^{3}+\frac {243}{2} x^{2}+54 x\) | \(30\) |
risch | \(-125 x^{6}-295 x^{5}-\frac {785}{4} x^{4}+51 x^{3}+\frac {243}{2} x^{2}+54 x\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 29, normalized size = 0.85 \begin {gather*} -125 \, x^{6} - 295 \, x^{5} - \frac {785}{4} \, x^{4} + 51 \, x^{3} + \frac {243}{2} \, x^{2} + 54 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.57, size = 29, normalized size = 0.85 \begin {gather*} -125 \, x^{6} - 295 \, x^{5} - \frac {785}{4} \, x^{4} + 51 \, x^{3} + \frac {243}{2} \, x^{2} + 54 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 31, normalized size = 0.91 \begin {gather*} - 125 x^{6} - 295 x^{5} - \frac {785 x^{4}}{4} + 51 x^{3} + \frac {243 x^{2}}{2} + 54 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.26, size = 29, normalized size = 0.85 \begin {gather*} -125 \, x^{6} - 295 \, x^{5} - \frac {785}{4} \, x^{4} + 51 \, x^{3} + \frac {243}{2} \, x^{2} + 54 \, 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 = 0.85 \begin {gather*} -125\,x^6-295\,x^5-\frac {785\,x^4}{4}+51\,x^3+\frac {243\,x^2}{2}+54\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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