Optimal. Leaf size=65 \[ -\frac {a^5}{15 x^{15}}-\frac {5 a^4 b}{12 x^{12}}-\frac {10 a^3 b^2}{9 x^9}-\frac {5 a^2 b^3}{3 x^6}-\frac {5 a b^4}{3 x^3}+b^5 \log (x) \]
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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*} -\frac {a^5}{15 x^{15}}-\frac {5 a^4 b}{12 x^{12}}-\frac {10 a^3 b^2}{9 x^9}-\frac {5 a^2 b^3}{3 x^6}-\frac {5 a b^4}{3 x^3}+b^5 \log (x) \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^{16}} \, dx &=\frac {1}{3} \text {Subst}\left (\int \frac {(a+b x)^5}{x^6} \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (\frac {a^5}{x^6}+\frac {5 a^4 b}{x^5}+\frac {10 a^3 b^2}{x^4}+\frac {10 a^2 b^3}{x^3}+\frac {5 a b^4}{x^2}+\frac {b^5}{x}\right ) \, dx,x,x^3\right )\\ &=-\frac {a^5}{15 x^{15}}-\frac {5 a^4 b}{12 x^{12}}-\frac {10 a^3 b^2}{9 x^9}-\frac {5 a^2 b^3}{3 x^6}-\frac {5 a b^4}{3 x^3}+b^5 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 65, normalized size = 1.00 \begin {gather*} -\frac {a^5}{15 x^{15}}-\frac {5 a^4 b}{12 x^{12}}-\frac {10 a^3 b^2}{9 x^9}-\frac {5 a^2 b^3}{3 x^6}-\frac {5 a b^4}{3 x^3}+b^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 | \(-\frac {a^{5}}{15 x^{15}}-\frac {5 a^{4} b}{12 x^{12}}-\frac {10 a^{3} b^{2}}{9 x^{9}}-\frac {5 a^{2} b^{3}}{3 x^{6}}-\frac {5 a \,b^{4}}{3 x^{3}}+b^{5} \ln \left (x \right )\) | \(56\) |
norman | \(\frac {-\frac {1}{15} a^{5}-\frac {5}{3} a \,b^{4} x^{12}-\frac {5}{3} a^{2} b^{3} x^{9}-\frac {10}{9} a^{3} b^{2} x^{6}-\frac {5}{12} a^{4} b \,x^{3}}{x^{15}}+b^{5} \ln \left (x \right )\) | \(58\) |
risch | \(\frac {-\frac {1}{15} a^{5}-\frac {5}{3} a \,b^{4} x^{12}-\frac {5}{3} a^{2} b^{3} x^{9}-\frac {10}{9} a^{3} b^{2} x^{6}-\frac {5}{12} a^{4} b \,x^{3}}{x^{15}}+b^{5} \ln \left (x \right )\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 61, normalized size = 0.94 \begin {gather*} \frac {1}{3} \, b^{5} \log \left (x^{3}\right ) - \frac {300 \, a b^{4} x^{12} + 300 \, a^{2} b^{3} x^{9} + 200 \, a^{3} b^{2} x^{6} + 75 \, a^{4} b x^{3} + 12 \, a^{5}}{180 \, x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 61, normalized size = 0.94 \begin {gather*} \frac {180 \, b^{5} x^{15} \log \left (x\right ) - 300 \, a b^{4} x^{12} - 300 \, a^{2} b^{3} x^{9} - 200 \, a^{3} b^{2} x^{6} - 75 \, a^{4} b x^{3} - 12 \, a^{5}}{180 \, x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.24, size = 61, normalized size = 0.94 \begin {gather*} b^{5} \log {\left (x \right )} + \frac {- 12 a^{5} - 75 a^{4} b x^{3} - 200 a^{3} b^{2} x^{6} - 300 a^{2} b^{3} x^{9} - 300 a b^{4} x^{12}}{180 x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.24, size = 67, normalized size = 1.03 \begin {gather*} b^{5} \log \left ({\left | x \right |}\right ) - \frac {137 \, b^{5} x^{15} + 300 \, a b^{4} x^{12} + 300 \, a^{2} b^{3} x^{9} + 200 \, a^{3} b^{2} x^{6} + 75 \, a^{4} b x^{3} + 12 \, a^{5}}{180 \, x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.01, size = 58, normalized size = 0.89 \begin {gather*} b^5\,\ln \left (x\right )-\frac {\frac {a^5}{15}+\frac {5\,a^4\,b\,x^3}{12}+\frac {10\,a^3\,b^2\,x^6}{9}+\frac {5\,a^2\,b^3\,x^9}{3}+\frac {5\,a\,b^4\,x^{12}}{3}}{x^{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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