Optimal. Leaf size=17 \[ \frac {a x^3}{3}+\frac {b x^4}{4} \]
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Rubi [A]
time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {45}
\begin {gather*} \frac {a x^3}{3}+\frac {b x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {align*} \int x^2 (a+b x) \, dx &=\int \left (a x^2+b x^3\right ) \, dx\\ &=\frac {a x^3}{3}+\frac {b x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {a x^3}{3}+\frac {b x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 14, normalized size = 0.82
method | result | size |
gosper | \(\frac {1}{3} a \,x^{3}+\frac {1}{4} b \,x^{4}\) | \(14\) |
default | \(\frac {1}{3} a \,x^{3}+\frac {1}{4} b \,x^{4}\) | \(14\) |
norman | \(\frac {1}{3} a \,x^{3}+\frac {1}{4} b \,x^{4}\) | \(14\) |
risch | \(\frac {1}{3} a \,x^{3}+\frac {1}{4} b \,x^{4}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, b x^{4} + \frac {1}{3} \, a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.55, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, b x^{4} + \frac {1}{3} \, a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.71 \begin {gather*} \frac {a x^{3}}{3} + \frac {b x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.37, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, b x^{4} + \frac {1}{3} \, a x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 13, normalized size = 0.76 \begin {gather*} \frac {x^3\,\left (4\,a+3\,b\,x\right )}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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