Optimal. Leaf size=25 \[ \frac {27 x^7}{7}+9 x^6+\frac {36 x^5}{5}+2 x^4 \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {611} \[ \frac {27 x^7}{7}+9 x^6+\frac {36 x^5}{5}+2 x^4 \]
Antiderivative was successfully verified.
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Rule 611
Rubi steps
\begin {align*} \int \left (2 x+3 x^2\right )^3 \, dx &=\int \left (8 x^3+36 x^4+54 x^5+27 x^6\right ) \, dx\\ &=2 x^4+\frac {36 x^5}{5}+9 x^6+\frac {27 x^7}{7}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 25, normalized size = 1.00 \[ \frac {27 x^7}{7}+9 x^6+\frac {36 x^5}{5}+2 x^4 \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 25, normalized size = 1.00 \[ \frac {1}{35} \left (135 x^7+315 x^6+252 x^5+70 x^4\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 21, normalized size = 0.84 \[ \frac {27}{7} x^{7} + 9 x^{6} + \frac {36}{5} x^{5} + 2 x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.94, size = 21, normalized size = 0.84 \[ \frac {27}{7} \, x^{7} + 9 \, x^{6} + \frac {36}{5} \, x^{5} + 2 \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.25, size = 21, normalized size = 0.84
method | result | size |
gosper | \(\frac {x^{4} \left (135 x^{3}+315 x^{2}+252 x +70\right )}{35}\) | \(21\) |
default | \(2 x^{4}+\frac {36}{5} x^{5}+9 x^{6}+\frac {27}{7} x^{7}\) | \(22\) |
norman | \(2 x^{4}+\frac {36}{5} x^{5}+9 x^{6}+\frac {27}{7} x^{7}\) | \(22\) |
risch | \(2 x^{4}+\frac {36}{5} x^{5}+9 x^{6}+\frac {27}{7} x^{7}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 21, normalized size = 0.84 \[ \frac {27}{7} \, x^{7} + 9 \, x^{6} + \frac {36}{5} \, x^{5} + 2 \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 21, normalized size = 0.84 \[ \frac {27\,x^7}{7}+9\,x^6+\frac {36\,x^5}{5}+2\,x^4 \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 22, normalized size = 0.88 \[ \frac {27 x^{7}}{7} + 9 x^{6} + \frac {36 x^{5}}{5} + 2 x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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