Optimal. Leaf size=16 \[ -\frac{1}{14 x^{14} \left (b+c x^2\right )^7} \]
[Out]
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Rubi [A] time = 0.0134463, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ -\frac{1}{14 x^{14} \left (b+c x^2\right )^7} \]
Antiderivative was successfully verified.
[In] Int[(b + 2*c*x^2)/(x^15*(b + c*x^2)^8),x]
[Out]
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Rubi in Sympy [A] time = 8.76833, size = 15, normalized size = 0.94 \[ - \frac{1}{14 x^{14} \left (b + c x^{2}\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*x**2+b)/x**15/(c*x**2+b)**8,x)
[Out]
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Mathematica [A] time = 0.054071, size = 16, normalized size = 1. \[ -\frac{1}{14 x^{14} \left (b+c x^2\right )^7} \]
Antiderivative was successfully verified.
[In] Integrate[(b + 2*c*x^2)/(x^15*(b + c*x^2)^8),x]
[Out]
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Maple [B] time = 0.027, size = 197, normalized size = 12.3 \[ -{\frac{1}{14\,{b}^{7}{x}^{14}}}-66\,{\frac{{c}^{6}}{{b}^{13}{x}^{2}}}+33\,{\frac{{c}^{5}}{{b}^{12}{x}^{4}}}-15\,{\frac{{c}^{4}}{{b}^{11}{x}^{6}}}+6\,{\frac{{c}^{3}}{{b}^{10}{x}^{8}}}-2\,{\frac{{c}^{2}}{{b}^{9}{x}^{10}}}+{\frac{c}{2\,{b}^{8}{x}^{12}}}-{\frac{{c}^{8}}{2\,{b}^{13}} \left ( -{\frac{{b}^{5}}{c \left ( c{x}^{2}+b \right ) ^{6}}}-132\,{\frac{1}{c \left ( c{x}^{2}+b \right ) }}-30\,{\frac{{b}^{2}}{c \left ( c{x}^{2}+b \right ) ^{3}}}-4\,{\frac{{b}^{4}}{c \left ( c{x}^{2}+b \right ) ^{5}}}-12\,{\frac{{b}^{3}}{c \left ( c{x}^{2}+b \right ) ^{4}}}-{\frac{{b}^{6}}{7\,c \left ( c{x}^{2}+b \right ) ^{7}}}-66\,{\frac{b}{c \left ( c{x}^{2}+b \right ) ^{2}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*x^2+b)/x^15/(c*x^2+b)^8,x)
[Out]
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Maxima [A] time = 1.44375, size = 109, normalized size = 6.81 \[ -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)/((c*x^2 + b)^8*x^15),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.222377, size = 109, normalized size = 6.81 \[ -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)/((c*x^2 + b)^8*x^15),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x**2+b)/x**15/(c*x**2+b)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.209942, size = 20, normalized size = 1.25 \[ -\frac{1}{14 \,{\left (c x^{4} + b x^{2}\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)/((c*x^2 + b)^8*x^15),x, algorithm="giac")
[Out]