Optimal. Leaf size=17 \[ \frac {b x^2}{2}+\frac {c x^4}{4} \]
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Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14}
\begin {gather*} \frac {b x^2}{2}+\frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {align*} \int \frac {b x^2+c x^4}{x} \, dx &=\int \left (b x+c x^3\right ) \, dx\\ &=\frac {b x^2}{2}+\frac {c x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {b x^2}{2}+\frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 15, normalized size = 0.88
method | result | size |
norman | \(\frac {1}{2} b \,x^{2}+\frac {1}{4} c \,x^{4}\) | \(14\) |
gosper | \(\frac {x^{2} \left (c \,x^{2}+2 b \right )}{4}\) | \(15\) |
default | \(\frac {\left (c \,x^{2}+b \right )^{2}}{4 c}\) | \(15\) |
risch | \(\frac {c \,x^{4}}{4}+\frac {b \,x^{2}}{2}+\frac {b^{2}}{4 c}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{2} \, b x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{2} \, b x^{2} \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 {b x^{2}}{2} + \frac {c x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.37, size = 13, normalized size = 0.76 \begin {gather*} \frac {1}{4} \, c x^{4} + \frac {1}{2} \, b x^{2} \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 {c\,x^4}{4}+\frac {b\,x^2}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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