Optimal. Leaf size=65 \[ \frac {5}{3} a^4 b x^3+\frac {5}{3} a^3 b^2 x^6+\frac {10}{9} a^2 b^3 x^9+\frac {5}{12} a b^4 x^{12}+\frac {b^5 x^{15}}{15}+a^5 \log (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 65, 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 = {272, 45}
\begin {gather*} a^5 \log (x)+\frac {5}{3} a^4 b x^3+\frac {5}{3} a^3 b^2 x^6+\frac {10}{9} a^2 b^3 x^9+\frac {5}{12} a b^4 x^{12}+\frac {b^5 x^{15}}{15} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int \frac {\left (a+b x^3\right )^5}{x} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^5}{x} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (5 a^4 b+\frac {a^5}{x}+10 a^3 b^2 x+10 a^2 b^3 x^2+5 a b^4 x^3+b^5 x^4\right ) \, dx,x,x^3\right )\\ &=\frac {5}{3} a^4 b x^3+\frac {5}{3} a^3 b^2 x^6+\frac {10}{9} a^2 b^3 x^9+\frac {5}{12} a b^4 x^{12}+\frac {b^5 x^{15}}{15}+a^5 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 65, normalized size = 1.00 \begin {gather*} \frac {5}{3} a^4 b x^3+\frac {5}{3} a^3 b^2 x^6+\frac {10}{9} a^2 b^3 x^9+\frac {5}{12} a b^4 x^{12}+\frac {b^5 x^{15}}{15}+a^5 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 56, normalized size = 0.86
method | result | size |
default | \(\frac {5 a^{4} b \,x^{3}}{3}+\frac {5 a^{3} b^{2} x^{6}}{3}+\frac {10 a^{2} b^{3} x^{9}}{9}+\frac {5 a \,b^{4} x^{12}}{12}+\frac {b^{5} x^{15}}{15}+a^{5} \ln \left (x \right )\) | \(56\) |
norman | \(\frac {5 a^{4} b \,x^{3}}{3}+\frac {5 a^{3} b^{2} x^{6}}{3}+\frac {10 a^{2} b^{3} x^{9}}{9}+\frac {5 a \,b^{4} x^{12}}{12}+\frac {b^{5} x^{15}}{15}+a^{5} \ln \left (x \right )\) | \(56\) |
risch | \(\frac {5 a^{4} b \,x^{3}}{3}+\frac {5 a^{3} b^{2} x^{6}}{3}+\frac {10 a^{2} b^{3} x^{9}}{9}+\frac {5 a \,b^{4} x^{12}}{12}+\frac {b^{5} x^{15}}{15}+a^{5} \ln \left (x \right )\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 58, normalized size = 0.89 \begin {gather*} \frac {1}{15} \, b^{5} x^{15} + \frac {5}{12} \, a b^{4} x^{12} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {5}{3} \, a^{3} b^{2} x^{6} + \frac {5}{3} \, a^{4} b x^{3} + \frac {1}{3} \, a^{5} \log \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 55, normalized size = 0.85 \begin {gather*} \frac {1}{15} \, b^{5} x^{15} + \frac {5}{12} \, a b^{4} x^{12} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {5}{3} \, a^{3} b^{2} x^{6} + \frac {5}{3} \, a^{4} b x^{3} + a^{5} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 65, normalized size = 1.00 \begin {gather*} a^{5} \log {\left (x \right )} + \frac {5 a^{4} b x^{3}}{3} + \frac {5 a^{3} b^{2} x^{6}}{3} + \frac {10 a^{2} b^{3} x^{9}}{9} + \frac {5 a b^{4} x^{12}}{12} + \frac {b^{5} x^{15}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.30, size = 56, normalized size = 0.86 \begin {gather*} \frac {1}{15} \, b^{5} x^{15} + \frac {5}{12} \, a b^{4} x^{12} + \frac {10}{9} \, a^{2} b^{3} x^{9} + \frac {5}{3} \, a^{3} b^{2} x^{6} + \frac {5}{3} \, a^{4} b x^{3} + a^{5} \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 55, normalized size = 0.85 \begin {gather*} a^5\,\ln \left (x\right )+\frac {b^5\,x^{15}}{15}+\frac {5\,a^4\,b\,x^3}{3}+\frac {5\,a\,b^4\,x^{12}}{12}+\frac {5\,a^3\,b^2\,x^6}{3}+\frac {10\,a^2\,b^3\,x^9}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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