Optimal. Leaf size=39 \[ a^3 \log (x)+\frac {3}{4} a^2 b x^4+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{12}}{12} \]
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Rubi [A] time = 0.02, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {3}{4} a^2 b x^4+a^3 \log (x)+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{12}}{12} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^4\right )^3}{x} \, dx &=\frac {1}{4} \operatorname {Subst}\left (\int \frac {(a+b x)^3}{x} \, dx,x,x^4\right )\\ &=\frac {1}{4} \operatorname {Subst}\left (\int \left (3 a^2 b+\frac {a^3}{x}+3 a b^2 x+b^3 x^2\right ) \, dx,x,x^4\right )\\ &=\frac {3}{4} a^2 b x^4+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{12}}{12}+a^3 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 39, normalized size = 1.00 \[ a^3 \log (x)+\frac {3}{4} a^2 b x^4+\frac {3}{8} a b^2 x^8+\frac {b^3 x^{12}}{12} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 33, normalized size = 0.85 \[ \frac {1}{12} \, b^{3} x^{12} + \frac {3}{8} \, a b^{2} x^{8} + \frac {3}{4} \, a^{2} b x^{4} + a^{3} \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 36, normalized size = 0.92 \[ \frac {1}{12} \, b^{3} x^{12} + \frac {3}{8} \, a b^{2} x^{8} + \frac {3}{4} \, a^{2} b x^{4} + \frac {1}{4} \, a^{3} \log \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 34, normalized size = 0.87 \[ \frac {b^{3} x^{12}}{12}+\frac {3 a \,b^{2} x^{8}}{8}+\frac {3 a^{2} b \,x^{4}}{4}+a^{3} \ln \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 36, normalized size = 0.92 \[ \frac {1}{12} \, b^{3} x^{12} + \frac {3}{8} \, a b^{2} x^{8} + \frac {3}{4} \, a^{2} b x^{4} + \frac {1}{4} \, a^{3} \log \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 33, normalized size = 0.85 \[ a^3\,\ln \relax (x)+\frac {b^3\,x^{12}}{12}+\frac {3\,a^2\,b\,x^4}{4}+\frac {3\,a\,b^2\,x^8}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 37, normalized size = 0.95 \[ a^{3} \log {\relax (x )} + \frac {3 a^{2} b x^{4}}{4} + \frac {3 a b^{2} x^{8}}{8} + \frac {b^{3} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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