Optimal. Leaf size=67 \[ -\frac {2 f^{a+\frac {b}{x^3}}}{3 b^3 \log ^3(f)}+\frac {2 f^{a+\frac {b}{x^3}}}{3 b^2 x^3 \log ^2(f)}-\frac {f^{a+\frac {b}{x^3}}}{3 b x^6 \log (f)} \]
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Rubi [A] time = 0.07, antiderivative size = 67, 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 = {2212, 2209} \[ \frac {2 f^{a+\frac {b}{x^3}}}{3 b^2 x^3 \log ^2(f)}-\frac {2 f^{a+\frac {b}{x^3}}}{3 b^3 \log ^3(f)}-\frac {f^{a+\frac {b}{x^3}}}{3 b x^6 \log (f)} \]
Antiderivative was successfully verified.
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Rule 2209
Rule 2212
Rubi steps
\begin {align*} \int \frac {f^{a+\frac {b}{x^3}}}{x^{10}} \, dx &=-\frac {f^{a+\frac {b}{x^3}}}{3 b x^6 \log (f)}-\frac {2 \int \frac {f^{a+\frac {b}{x^3}}}{x^7} \, dx}{b \log (f)}\\ &=\frac {2 f^{a+\frac {b}{x^3}}}{3 b^2 x^3 \log ^2(f)}-\frac {f^{a+\frac {b}{x^3}}}{3 b x^6 \log (f)}+\frac {2 \int \frac {f^{a+\frac {b}{x^3}}}{x^4} \, dx}{b^2 \log ^2(f)}\\ &=-\frac {2 f^{a+\frac {b}{x^3}}}{3 b^3 \log ^3(f)}+\frac {2 f^{a+\frac {b}{x^3}}}{3 b^2 x^3 \log ^2(f)}-\frac {f^{a+\frac {b}{x^3}}}{3 b x^6 \log (f)}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 45, normalized size = 0.67 \[ -\frac {f^{a+\frac {b}{x^3}} \left (b^2 \log ^2(f)-2 b x^3 \log (f)+2 x^6\right )}{3 b^3 x^6 \log ^3(f)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 47, normalized size = 0.70 \[ -\frac {{\left (2 \, x^{6} - 2 \, b x^{3} \log \relax (f) + b^{2} \log \relax (f)^{2}\right )} f^{\frac {a x^{3} + b}{x^{3}}}}{3 \, b^{3} x^{6} \log \relax (f)^{3}} \]
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 \[ \int \frac {f^{a + \frac {b}{x^{3}}}}{x^{10}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 75, normalized size = 1.12 \[ \frac {-\frac {2 x^{9} {\mathrm e}^{\left (a +\frac {b}{x^{3}}\right ) \ln \relax (f )}}{3 b^{3} \ln \relax (f )^{3}}+\frac {2 x^{6} {\mathrm e}^{\left (a +\frac {b}{x^{3}}\right ) \ln \relax (f )}}{3 b^{2} \ln \relax (f )^{2}}-\frac {x^{3} {\mathrm e}^{\left (a +\frac {b}{x^{3}}\right ) \ln \relax (f )}}{3 b \ln \relax (f )}}{x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 1.31, size = 22, normalized size = 0.33 \[ -\frac {f^{a} \Gamma \left (3, -\frac {b \log \relax (f)}{x^{3}}\right )}{3 \, b^{3} \log \relax (f)^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.54, size = 48, normalized size = 0.72 \[ -\frac {f^{a+\frac {b}{x^3}}\,\left (\frac {1}{3\,b\,\ln \relax (f)}-\frac {2\,x^3}{3\,b^2\,{\ln \relax (f)}^2}+\frac {2\,x^6}{3\,b^3\,{\ln \relax (f)}^3}\right )}{x^6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 44, normalized size = 0.66 \[ \frac {f^{a + \frac {b}{x^{3}}} \left (- b^{2} \log {\relax (f )}^{2} + 2 b x^{3} \log {\relax (f )} - 2 x^{6}\right )}{3 b^{3} x^{6} \log {\relax (f )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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