Optimal. Leaf size=31 \[ 36 x+78 x^2+\frac {85 x^3}{3}-128 x^4-183 x^5-75 x^6 \]
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Rubi [A]
time = 0.01, antiderivative size = 31, 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*} -75 x^6-183 x^5-128 x^4+\frac {85 x^3}{3}+78 x^2+36 x \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x) (2+3 x)^2 (3+5 x)^2 \, dx &=\int \left (36+156 x+85 x^2-512 x^3-915 x^4-450 x^5\right ) \, dx\\ &=36 x+78 x^2+\frac {85 x^3}{3}-128 x^4-183 x^5-75 x^6\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 31, normalized size = 1.00 \begin {gather*} 36 x+78 x^2+\frac {85 x^3}{3}-128 x^4-183 x^5-75 x^6 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 30, normalized size = 0.97
method | result | size |
gosper | \(-\frac {x \left (225 x^{5}+549 x^{4}+384 x^{3}-85 x^{2}-234 x -108\right )}{3}\) | \(29\) |
default | \(36 x +78 x^{2}+\frac {85}{3} x^{3}-128 x^{4}-183 x^{5}-75 x^{6}\) | \(30\) |
norman | \(36 x +78 x^{2}+\frac {85}{3} x^{3}-128 x^{4}-183 x^{5}-75 x^{6}\) | \(30\) |
risch | \(36 x +78 x^{2}+\frac {85}{3} x^{3}-128 x^{4}-183 x^{5}-75 x^{6}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 29, normalized size = 0.94 \begin {gather*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.23, size = 29, normalized size = 0.94 \begin {gather*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 29, normalized size = 0.94 \begin {gather*} - 75 x^{6} - 183 x^{5} - 128 x^{4} + \frac {85 x^{3}}{3} + 78 x^{2} + 36 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.36, size = 29, normalized size = 0.94 \begin {gather*} -75 \, x^{6} - 183 \, x^{5} - 128 \, x^{4} + \frac {85}{3} \, x^{3} + 78 \, x^{2} + 36 \, 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 = 0.94 \begin {gather*} -75\,x^6-183\,x^5-128\,x^4+\frac {85\,x^3}{3}+78\,x^2+36\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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