Optimal. Leaf size=63 \[ \frac{b^3 \log \left (a+b x^5\right )}{5 a^4}-\frac{b^3 \log (x)}{a^4}-\frac{b^2}{5 a^3 x^5}+\frac{b}{10 a^2 x^{10}}-\frac{1}{15 a x^{15}} \]
[Out]
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Rubi [A] time = 0.0801135, antiderivative size = 63, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{b^3 \log \left (a+b x^5\right )}{5 a^4}-\frac{b^3 \log (x)}{a^4}-\frac{b^2}{5 a^3 x^5}+\frac{b}{10 a^2 x^{10}}-\frac{1}{15 a x^{15}} \]
Antiderivative was successfully verified.
[In] Int[1/(x^16*(a + b*x^5)),x]
[Out]
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Rubi in Sympy [A] time = 12.5634, size = 60, normalized size = 0.95 \[ - \frac{1}{15 a x^{15}} + \frac{b}{10 a^{2} x^{10}} - \frac{b^{2}}{5 a^{3} x^{5}} - \frac{b^{3} \log{\left (x^{5} \right )}}{5 a^{4}} + \frac{b^{3} \log{\left (a + b x^{5} \right )}}{5 a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**16/(b*x**5+a),x)
[Out]
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Mathematica [A] time = 0.0121859, size = 63, normalized size = 1. \[ \frac{b^3 \log \left (a+b x^5\right )}{5 a^4}-\frac{b^3 \log (x)}{a^4}-\frac{b^2}{5 a^3 x^5}+\frac{b}{10 a^2 x^{10}}-\frac{1}{15 a x^{15}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^16*(a + b*x^5)),x]
[Out]
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Maple [A] time = 0.011, size = 56, normalized size = 0.9 \[ -{\frac{1}{15\,a{x}^{15}}}+{\frac{b}{10\,{a}^{2}{x}^{10}}}-{\frac{{b}^{2}}{5\,{a}^{3}{x}^{5}}}-{\frac{{b}^{3}\ln \left ( x \right ) }{{a}^{4}}}+{\frac{{b}^{3}\ln \left ( b{x}^{5}+a \right ) }{5\,{a}^{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^16/(b*x^5+a),x)
[Out]
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Maxima [A] time = 1.41469, size = 78, normalized size = 1.24 \[ \frac{b^{3} \log \left (b x^{5} + a\right )}{5 \, a^{4}} - \frac{b^{3} \log \left (x^{5}\right )}{5 \, a^{4}} - \frac{6 \, b^{2} x^{10} - 3 \, a b x^{5} + 2 \, a^{2}}{30 \, a^{3} x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^16),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222387, size = 78, normalized size = 1.24 \[ \frac{6 \, b^{3} x^{15} \log \left (b x^{5} + a\right ) - 30 \, b^{3} x^{15} \log \left (x\right ) - 6 \, a b^{2} x^{10} + 3 \, a^{2} b x^{5} - 2 \, a^{3}}{30 \, a^{4} x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^16),x, algorithm="fricas")
[Out]
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Sympy [A] time = 157.098, size = 56, normalized size = 0.89 \[ - \frac{2 a^{2} - 3 a b x^{5} + 6 b^{2} x^{10}}{30 a^{3} x^{15}} - \frac{b^{3} \log{\left (x \right )}}{a^{4}} + \frac{b^{3} \log{\left (\frac{a}{b} + x^{5} \right )}}{5 a^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**16/(b*x**5+a),x)
[Out]
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GIAC/XCAS [A] time = 0.238044, size = 93, normalized size = 1.48 \[ \frac{b^{3}{\rm ln}\left ({\left | b x^{5} + a \right |}\right )}{5 \, a^{4}} - \frac{b^{3}{\rm ln}\left ({\left | x \right |}\right )}{a^{4}} + \frac{11 \, b^{3} x^{15} - 6 \, a b^{2} x^{10} + 3 \, a^{2} b x^{5} - 2 \, a^{3}}{30 \, a^{4} x^{15}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x^5 + a)*x^16),x, algorithm="giac")
[Out]