Optimal. Leaf size=25 \[ \frac {a x^2}{2}+\frac {b x^3}{3}+\frac {c x^4}{4} \]
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Rubi [A]
time = 0.00, antiderivative size = 25, 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 = {14}
\begin {gather*} \frac {a x^2}{2}+\frac {b x^3}{3}+\frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {a x^2+b x^3+c x^4}{x} \, dx &=\int \left (a x+b x^2+c x^3\right ) \, dx\\ &=\frac {a x^2}{2}+\frac {b x^3}{3}+\frac {c x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} \frac {a x^2}{2}+\frac {b x^3}{3}+\frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 20, normalized size = 0.80
method | result | size |
gosper | \(\frac {x^{2} \left (3 c \,x^{2}+4 b x +6 a \right )}{12}\) | \(20\) |
default | \(\frac {1}{2} a \,x^{2}+\frac {1}{3} b \,x^{3}+\frac {1}{4} c \,x^{4}\) | \(20\) |
norman | \(\frac {1}{2} a \,x^{2}+\frac {1}{3} b \,x^{3}+\frac {1}{4} c \,x^{4}\) | \(20\) |
risch | \(\frac {1}{2} a \,x^{2}+\frac {1}{3} b \,x^{3}+\frac {1}{4} c \,x^{4}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{3} \, b x^{3} + \frac {1}{2} \, a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{3} \, b x^{3} + \frac {1}{2} \, a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 19, normalized size = 0.76 \begin {gather*} \frac {a x^{2}}{2} + \frac {b x^{3}}{3} + \frac {c x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.21, size = 19, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{3} \, b x^{3} + \frac {1}{2} \, a x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 19, normalized size = 0.76 \begin {gather*} \frac {x^2\,\left (3\,c\,x^2+4\,b\,x+6\,a\right )}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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