Optimal. Leaf size=17 \[ \frac {a x^3}{3}+\frac {b x^4}{4} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \frac {a x^3}{3}+\frac {b x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {align*} \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 = 0.02, size = 14, normalized size = 0.82
method | result | size |
gosper | \(\frac {x^{3} \left (3 b x +4 a \right )}{12}\) | \(14\) |
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 = 3.56, 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 = 1.46, 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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