Optimal. Leaf size=23 \[ \frac {11}{100} (3+5 x)^4-\frac {2}{125} (3+5 x)^5 \]
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Rubi [A]
time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {45}
\begin {gather*} \frac {11}{100} (5 x+3)^4-\frac {2}{125} (5 x+3)^5 \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (1-2 x) (3+5 x)^3 \, dx &=\int \left (\frac {11}{5} (3+5 x)^3-\frac {2}{5} (3+5 x)^4\right ) \, dx\\ &=\frac {11}{100} (3+5 x)^4-\frac {2}{125} (3+5 x)^5\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 28, normalized size = 1.22 \begin {gather*} 27 x+\frac {81 x^2}{2}-15 x^3-\frac {325 x^4}{4}-50 x^5 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 25, normalized size = 1.09
method | result | size |
gosper | \(-\frac {x \left (200 x^{4}+325 x^{3}+60 x^{2}-162 x -108\right )}{4}\) | \(24\) |
default | \(-50 x^{5}-\frac {325}{4} x^{4}-15 x^{3}+\frac {81}{2} x^{2}+27 x\) | \(25\) |
norman | \(-50 x^{5}-\frac {325}{4} x^{4}-15 x^{3}+\frac {81}{2} x^{2}+27 x\) | \(25\) |
risch | \(-50 x^{5}-\frac {325}{4} x^{4}-15 x^{3}+\frac {81}{2} x^{2}+27 x\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 24, normalized size = 1.04 \begin {gather*} -50 \, x^{5} - \frac {325}{4} \, x^{4} - 15 \, x^{3} + \frac {81}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.69, size = 24, normalized size = 1.04 \begin {gather*} -50 \, x^{5} - \frac {325}{4} \, x^{4} - 15 \, x^{3} + \frac {81}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 26, normalized size = 1.13 \begin {gather*} - 50 x^{5} - \frac {325 x^{4}}{4} - 15 x^{3} + \frac {81 x^{2}}{2} + 27 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.97, size = 24, normalized size = 1.04 \begin {gather*} -50 \, x^{5} - \frac {325}{4} \, x^{4} - 15 \, x^{3} + \frac {81}{2} \, x^{2} + 27 \, 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 = 1.04 \begin {gather*} -50\,x^5-\frac {325\,x^4}{4}-15\,x^3+\frac {81\,x^2}{2}+27\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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