Optimal. Leaf size=51 \[ 72 x+138 x^2-\frac {202 x^3}{3}-\frac {2045 x^4}{4}-\frac {1828 x^5}{5}+\frac {1029 x^6}{2}+\frac {5940 x^7}{7}+\frac {675 x^8}{2} \]
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Rubi [A]
time = 0.01, antiderivative size = 51, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {675 x^8}{2}+\frac {5940 x^7}{7}+\frac {1029 x^6}{2}-\frac {1828 x^5}{5}-\frac {2045 x^4}{4}-\frac {202 x^3}{3}+138 x^2+72 x \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^3 (3+5 x)^2 \, dx &=\int \left (72+276 x-202 x^2-2045 x^3-1828 x^4+3087 x^5+5940 x^6+2700 x^7\right ) \, dx\\ &=72 x+138 x^2-\frac {202 x^3}{3}-\frac {2045 x^4}{4}-\frac {1828 x^5}{5}+\frac {1029 x^6}{2}+\frac {5940 x^7}{7}+\frac {675 x^8}{2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 51, normalized size = 1.00 \begin {gather*} 72 x+138 x^2-\frac {202 x^3}{3}-\frac {2045 x^4}{4}-\frac {1828 x^5}{5}+\frac {1029 x^6}{2}+\frac {5940 x^7}{7}+\frac {675 x^8}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 40, normalized size = 0.78
method | result | size |
gosper | \(\frac {x \left (141750 x^{7}+356400 x^{6}+216090 x^{5}-153552 x^{4}-214725 x^{3}-28280 x^{2}+57960 x +30240\right )}{420}\) | \(39\) |
default | \(72 x +138 x^{2}-\frac {202}{3} x^{3}-\frac {2045}{4} x^{4}-\frac {1828}{5} x^{5}+\frac {1029}{2} x^{6}+\frac {5940}{7} x^{7}+\frac {675}{2} x^{8}\) | \(40\) |
norman | \(72 x +138 x^{2}-\frac {202}{3} x^{3}-\frac {2045}{4} x^{4}-\frac {1828}{5} x^{5}+\frac {1029}{2} x^{6}+\frac {5940}{7} x^{7}+\frac {675}{2} x^{8}\) | \(40\) |
risch | \(72 x +138 x^{2}-\frac {202}{3} x^{3}-\frac {2045}{4} x^{4}-\frac {1828}{5} x^{5}+\frac {1029}{2} x^{6}+\frac {5940}{7} x^{7}+\frac {675}{2} x^{8}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 39, normalized size = 0.76 \begin {gather*} \frac {675}{2} \, x^{8} + \frac {5940}{7} \, x^{7} + \frac {1029}{2} \, x^{6} - \frac {1828}{5} \, x^{5} - \frac {2045}{4} \, x^{4} - \frac {202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 39, normalized size = 0.76 \begin {gather*} \frac {675}{2} \, x^{8} + \frac {5940}{7} \, x^{7} + \frac {1029}{2} \, x^{6} - \frac {1828}{5} \, x^{5} - \frac {2045}{4} \, x^{4} - \frac {202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 48, normalized size = 0.94 \begin {gather*} \frac {675 x^{8}}{2} + \frac {5940 x^{7}}{7} + \frac {1029 x^{6}}{2} - \frac {1828 x^{5}}{5} - \frac {2045 x^{4}}{4} - \frac {202 x^{3}}{3} + 138 x^{2} + 72 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.62, size = 39, normalized size = 0.76 \begin {gather*} \frac {675}{2} \, x^{8} + \frac {5940}{7} \, x^{7} + \frac {1029}{2} \, x^{6} - \frac {1828}{5} \, x^{5} - \frac {2045}{4} \, x^{4} - \frac {202}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 39, normalized size = 0.76 \begin {gather*} \frac {675\,x^8}{2}+\frac {5940\,x^7}{7}+\frac {1029\,x^6}{2}-\frac {1828\,x^5}{5}-\frac {2045\,x^4}{4}-\frac {202\,x^3}{3}+138\,x^2+72\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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