Optimal. Leaf size=65 \[ -\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{8 x^8}-\frac {5 a^3 b^2}{3 x^6}-\frac {5 a^2 b^3}{2 x^4}-\frac {5 a b^4}{2 x^2}+b^5 \log (x) \]
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Rubi [A] time = 0.03, 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 = {266, 43} \[ -\frac {5 a^3 b^2}{3 x^6}-\frac {5 a^2 b^3}{2 x^4}-\frac {5 a^4 b}{8 x^8}-\frac {a^5}{10 x^{10}}-\frac {5 a b^4}{2 x^2}+b^5 \log (x) \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {\left (a+b x^2\right )^5}{x^{11}} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^5}{x^6} \, dx,x,x^2\right )\\ &=\frac {1}{2} \operatorname {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^2\right )\\ &=-\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{8 x^8}-\frac {5 a^3 b^2}{3 x^6}-\frac {5 a^2 b^3}{2 x^4}-\frac {5 a b^4}{2 x^2}+b^5 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 65, normalized size = 1.00 \[ -\frac {a^5}{10 x^{10}}-\frac {5 a^4 b}{8 x^8}-\frac {5 a^3 b^2}{3 x^6}-\frac {5 a^2 b^3}{2 x^4}-\frac {5 a b^4}{2 x^2}+b^5 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 61, normalized size = 0.94 \[ \frac {120 \, b^{5} x^{10} \log \relax (x) - 300 \, a b^{4} x^{8} - 300 \, a^{2} b^{3} x^{6} - 200 \, a^{3} b^{2} x^{4} - 75 \, a^{4} b x^{2} - 12 \, a^{5}}{120 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 69, normalized size = 1.06 \[ \frac {1}{2} \, b^{5} \log \left (x^{2}\right ) - \frac {137 \, b^{5} x^{10} + 300 \, a b^{4} x^{8} + 300 \, a^{2} b^{3} x^{6} + 200 \, a^{3} b^{2} x^{4} + 75 \, a^{4} b x^{2} + 12 \, a^{5}}{120 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 56, normalized size = 0.86 \[ b^{5} \ln \relax (x )-\frac {5 a \,b^{4}}{2 x^{2}}-\frac {5 a^{2} b^{3}}{2 x^{4}}-\frac {5 a^{3} b^{2}}{3 x^{6}}-\frac {5 a^{4} b}{8 x^{8}}-\frac {a^{5}}{10 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 61, normalized size = 0.94 \[ \frac {1}{2} \, b^{5} \log \left (x^{2}\right ) - \frac {300 \, a b^{4} x^{8} + 300 \, a^{2} b^{3} x^{6} + 200 \, a^{3} b^{2} x^{4} + 75 \, a^{4} b x^{2} + 12 \, a^{5}}{120 \, x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.77, size = 58, normalized size = 0.89 \[ b^5\,\ln \relax (x)-\frac {\frac {a^5}{10}+\frac {5\,a^4\,b\,x^2}{8}+\frac {5\,a^3\,b^2\,x^4}{3}+\frac {5\,a^2\,b^3\,x^6}{2}+\frac {5\,a\,b^4\,x^8}{2}}{x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.44, size = 61, normalized size = 0.94 \[ b^{5} \log {\relax (x )} + \frac {- 12 a^{5} - 75 a^{4} b x^{2} - 200 a^{3} b^{2} x^{4} - 300 a^{2} b^{3} x^{6} - 300 a b^{4} x^{8}}{120 x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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