Optimal. Leaf size=34 \[ \frac {121}{500} (3+5 x)^4-\frac {44}{625} (3+5 x)^5+\frac {2}{375} (3+5 x)^6 \]
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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 = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {45}
\begin {gather*} \frac {2}{375} (5 x+3)^6-\frac {44}{625} (5 x+3)^5+\frac {121}{500} (5 x+3)^4 \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int (1-2 x)^2 (3+5 x)^3 \, dx &=\int \left (\frac {121}{25} (3+5 x)^3-\frac {44}{25} (3+5 x)^4+\frac {4}{25} (3+5 x)^5\right ) \, dx\\ &=\frac {121}{500} (3+5 x)^4-\frac {44}{625} (3+5 x)^5+\frac {2}{375} (3+5 x)^6\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 35, normalized size = 1.03 \begin {gather*} 27 x+\frac {27 x^2}{2}-69 x^3-\frac {235 x^4}{4}+80 x^5+\frac {250 x^6}{3} \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 | \(\frac {x \left (1000 x^{5}+960 x^{4}-705 x^{3}-828 x^{2}+162 x +324\right )}{12}\) | \(29\) |
default | \(\frac {250}{3} x^{6}+80 x^{5}-\frac {235}{4} x^{4}-69 x^{3}+\frac {27}{2} x^{2}+27 x\) | \(30\) |
norman | \(\frac {250}{3} x^{6}+80 x^{5}-\frac {235}{4} x^{4}-69 x^{3}+\frac {27}{2} x^{2}+27 x\) | \(30\) |
risch | \(\frac {250}{3} x^{6}+80 x^{5}-\frac {235}{4} x^{4}-69 x^{3}+\frac {27}{2} x^{2}+27 x\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 29, normalized size = 0.85 \begin {gather*} \frac {250}{3} \, x^{6} + 80 \, x^{5} - \frac {235}{4} \, x^{4} - 69 \, x^{3} + \frac {27}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 29, normalized size = 0.85 \begin {gather*} \frac {250}{3} \, x^{6} + 80 \, x^{5} - \frac {235}{4} \, x^{4} - 69 \, x^{3} + \frac {27}{2} \, x^{2} + 27 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 32, normalized size = 0.94 \begin {gather*} \frac {250 x^{6}}{3} + 80 x^{5} - \frac {235 x^{4}}{4} - 69 x^{3} + \frac {27 x^{2}}{2} + 27 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.11, size = 29, normalized size = 0.85 \begin {gather*} \frac {250}{3} \, x^{6} + 80 \, x^{5} - \frac {235}{4} \, x^{4} - 69 \, x^{3} + \frac {27}{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 = 29, normalized size = 0.85 \begin {gather*} \frac {250\,x^6}{3}+80\,x^5-\frac {235\,x^4}{4}-69\,x^3+\frac {27\,x^2}{2}+27\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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