Optimal. Leaf size=8 \[ \frac {c x^4}{4} \]
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Rubi [A]
time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {21, 30}
\begin {gather*} \frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Rule 21
Rule 30
Rubi steps
\begin {align*} \int \frac {x^3 \left (a c+b c x^2\right )}{a+b x^2} \, dx &=c \int x^3 \, dx\\ &=\frac {c x^4}{4}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {c x^4}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 7, normalized size = 0.88
method | result | size |
gosper | \(\frac {x^{4} c}{4}\) | \(7\) |
default | \(\frac {x^{4} c}{4}\) | \(7\) |
norman | \(\frac {x^{4} c}{4}\) | \(7\) |
risch | \(\frac {x^{4} c}{4}\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 6, normalized size = 0.75 \begin {gather*} \frac {1}{4} \, c x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.80, size = 6, normalized size = 0.75 \begin {gather*} \frac {1}{4} \, c x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 5, normalized size = 0.62 \begin {gather*} \frac {c x^{4}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 6, normalized size = 0.75 \begin {gather*} \frac {1}{4} \, c x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.01, size = 6, normalized size = 0.75 \begin {gather*} \frac {c\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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