Optimal. Leaf size=42 \[ 54 x+\frac {135 x^2}{2}-111 x^3-\frac {1091 x^4}{4}+19 x^5+\frac {1100 x^6}{3}+\frac {1500 x^7}{7} \]
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Rubi [A]
time = 0.01, antiderivative size = 42, 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*} \frac {1500 x^7}{7}+\frac {1100 x^6}{3}+19 x^5-\frac {1091 x^4}{4}-111 x^3+\frac {135 x^2}{2}+54 x \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x) (3+5 x)^3 \, dx &=\int \left (54+135 x-333 x^2-1091 x^3+95 x^4+2200 x^5+1500 x^6\right ) \, dx\\ &=54 x+\frac {135 x^2}{2}-111 x^3-\frac {1091 x^4}{4}+19 x^5+\frac {1100 x^6}{3}+\frac {1500 x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 42, normalized size = 1.00 \begin {gather*} 54 x+\frac {135 x^2}{2}-111 x^3-\frac {1091 x^4}{4}+19 x^5+\frac {1100 x^6}{3}+\frac {1500 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.07, size = 35, normalized size = 0.83
method | result | size |
gosper | \(\frac {x \left (18000 x^{6}+30800 x^{5}+1596 x^{4}-22911 x^{3}-9324 x^{2}+5670 x +4536\right )}{84}\) | \(34\) |
default | \(54 x +\frac {135}{2} x^{2}-111 x^{3}-\frac {1091}{4} x^{4}+19 x^{5}+\frac {1100}{3} x^{6}+\frac {1500}{7} x^{7}\) | \(35\) |
norman | \(54 x +\frac {135}{2} x^{2}-111 x^{3}-\frac {1091}{4} x^{4}+19 x^{5}+\frac {1100}{3} x^{6}+\frac {1500}{7} x^{7}\) | \(35\) |
risch | \(54 x +\frac {135}{2} x^{2}-111 x^{3}-\frac {1091}{4} x^{4}+19 x^{5}+\frac {1100}{3} x^{6}+\frac {1500}{7} x^{7}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 34, normalized size = 0.81 \begin {gather*} \frac {1500}{7} \, x^{7} + \frac {1100}{3} \, x^{6} + 19 \, x^{5} - \frac {1091}{4} \, x^{4} - 111 \, x^{3} + \frac {135}{2} \, x^{2} + 54 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 34, normalized size = 0.81 \begin {gather*} \frac {1500}{7} \, x^{7} + \frac {1100}{3} \, x^{6} + 19 \, x^{5} - \frac {1091}{4} \, x^{4} - 111 \, x^{3} + \frac {135}{2} \, x^{2} + 54 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 39, normalized size = 0.93 \begin {gather*} \frac {1500 x^{7}}{7} + \frac {1100 x^{6}}{3} + 19 x^{5} - \frac {1091 x^{4}}{4} - 111 x^{3} + \frac {135 x^{2}}{2} + 54 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.22, size = 34, normalized size = 0.81 \begin {gather*} \frac {1500}{7} \, x^{7} + \frac {1100}{3} \, x^{6} + 19 \, x^{5} - \frac {1091}{4} \, x^{4} - 111 \, x^{3} + \frac {135}{2} \, x^{2} + 54 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 34, normalized size = 0.81 \begin {gather*} \frac {1500\,x^7}{7}+\frac {1100\,x^6}{3}+19\,x^5-\frac {1091\,x^4}{4}-111\,x^3+\frac {135\,x^2}{2}+54\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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