Optimal. Leaf size=16 \[ -\frac {1}{8 c \left (a+c x^4\right )^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {267}
\begin {gather*} -\frac {1}{8 c \left (a+c x^4\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x^3}{\left (a+c x^4\right )^3} \, dx &=-\frac {1}{8 c \left (a+c x^4\right )^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 16, normalized size = 1.00 \begin {gather*} -\frac {1}{8 c \left (a+c x^4\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 15, normalized size = 0.94
method | result | size |
gosper | \(-\frac {1}{8 c \left (x^{4} c +a \right )^{2}}\) | \(15\) |
derivativedivides | \(-\frac {1}{8 c \left (x^{4} c +a \right )^{2}}\) | \(15\) |
default | \(-\frac {1}{8 c \left (x^{4} c +a \right )^{2}}\) | \(15\) |
norman | \(-\frac {1}{8 c \left (x^{4} c +a \right )^{2}}\) | \(15\) |
risch | \(-\frac {1}{8 c \left (x^{4} c +a \right )^{2}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{8 \, {\left (c x^{4} + a\right )}^{2} c} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 26, normalized size = 1.62 \begin {gather*} -\frac {1}{8 \, {\left (c^{3} x^{8} + 2 \, a c^{2} x^{4} + a^{2} c\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 27, normalized size = 1.69 \begin {gather*} - \frac {1}{8 a^{2} c + 16 a c^{2} x^{4} + 8 c^{3} x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{8 \, {\left (c x^{4} + a\right )}^{2} c} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 25, normalized size = 1.56 \begin {gather*} -\frac {1}{8\,c\,\left (a^2+2\,a\,c\,x^4+c^2\,x^8\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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