Optimal. Leaf size=21 \[ -\frac {\left (a+b x^4\right )^{3/4}}{3 a x^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {270}
\begin {gather*} -\frac {\left (a+b x^4\right )^{3/4}}{3 a x^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {1}{x^4 \sqrt [4]{a+b x^4}} \, dx &=-\frac {\left (a+b x^4\right )^{3/4}}{3 a x^3}\\ \end {align*}
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Mathematica [A]
time = 0.13, size = 21, normalized size = 1.00 \begin {gather*} -\frac {\left (a+b x^4\right )^{3/4}}{3 a x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 18, normalized size = 0.86
method | result | size |
gosper | \(-\frac {\left (b \,x^{4}+a \right )^{\frac {3}{4}}}{3 a \,x^{3}}\) | \(18\) |
trager | \(-\frac {\left (b \,x^{4}+a \right )^{\frac {3}{4}}}{3 a \,x^{3}}\) | \(18\) |
risch | \(-\frac {\left (b \,x^{4}+a \right )^{\frac {3}{4}}}{3 a \,x^{3}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 17, normalized size = 0.81 \begin {gather*} -\frac {{\left (b x^{4} + a\right )}^{\frac {3}{4}}}{3 \, a x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 17, normalized size = 0.81 \begin {gather*} -\frac {{\left (b x^{4} + a\right )}^{\frac {3}{4}}}{3 \, a x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.36, size = 31, normalized size = 1.48 \begin {gather*} \frac {b^{\frac {3}{4}} \left (\frac {a}{b x^{4}} + 1\right )^{\frac {3}{4}} \Gamma \left (- \frac {3}{4}\right )}{4 a \Gamma \left (\frac {1}{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 17, normalized size = 0.81 \begin {gather*} -\frac {{\left (b\,x^4+a\right )}^{3/4}}{3\,a\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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