Optimal. Leaf size=20 \[ -\frac {f^{a+\frac {b}{x^3}}}{3 b \log (f)} \]
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Rubi [A]
time = 0.01, antiderivative size = 20, 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 = {2240}
\begin {gather*} -\frac {f^{a+\frac {b}{x^3}}}{3 b \log (f)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2240
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^3}}}{x^4} \, dx &=-\frac {f^{a+\frac {b}{x^3}}}{3 b \log (f)}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 20, normalized size = 1.00 \begin {gather*} -\frac {f^{a+\frac {b}{x^3}}}{3 b \log (f)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 19, normalized size = 0.95
method | result | size |
derivativedivides | \(-\frac {f^{a +\frac {b}{x^{3}}}}{3 b \ln \left (f \right )}\) | \(19\) |
default | \(-\frac {f^{a +\frac {b}{x^{3}}}}{3 b \ln \left (f \right )}\) | \(19\) |
norman | \(-\frac {{\mathrm e}^{\left (a +\frac {b}{x^{3}}\right ) \ln \left (f \right )}}{3 \ln \left (f \right ) b}\) | \(21\) |
risch | \(-\frac {f^{\frac {a \,x^{3}+b}{x^{3}}}}{3 \ln \left (f \right ) b}\) | \(23\) |
meijerg | \(\frac {f^{a} \left (1-{\mathrm e}^{\frac {b \ln \left (f \right )}{x^{3}}}\right )}{3 b \ln \left (f \right )}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 18, normalized size = 0.90 \begin {gather*} -\frac {f^{a + \frac {b}{x^{3}}}}{3 \, b \log \left (f\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 22, normalized size = 1.10 \begin {gather*} -\frac {f^{\frac {a x^{3} + b}{x^{3}}}}{3 \, b \log \left (f\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 27, normalized size = 1.35 \begin {gather*} \begin {cases} - \frac {f^{a + \frac {b}{x^{3}}}}{3 b \log {\left (f \right )}} & \text {for}\: b \log {\left (f \right )} \neq 0 \\- \frac {1}{3 x^{3}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.81, size = 22, normalized size = 1.10 \begin {gather*} -\frac {f^{\frac {a x^{3} + b}{x^{3}}}}{3 \, b \log \left (f\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.44, size = 18, normalized size = 0.90 \begin {gather*} -\frac {f^{a+\frac {b}{x^3}}}{3\,b\,\ln \left (f\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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