Optimal. Leaf size=18 \[ -\frac{1}{14 x^7 \left (b x+c x^3\right )^7} \]
[Out]
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Rubi [A] time = 0.0145864, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043 \[ -\frac{1}{14 x^7 \left (b x+c x^3\right )^7} \]
Antiderivative was successfully verified.
[In] Int[(b + 2*c*x^2)/(x^7*(b*x + c*x^3)^8),x]
[Out]
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Rubi in Sympy [A] time = 12.5887, size = 15, normalized size = 0.83 \[ - \frac{1}{14 x^{14} \left (b + c x^{2}\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*x**2+b)/x**7/(c*x**3+b*x)**8,x)
[Out]
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Mathematica [A] time = 0.0482352, size = 16, normalized size = 0.89 \[ -\frac{1}{14 x^{14} \left (b+c x^2\right )^7} \]
Antiderivative was successfully verified.
[In] Integrate[(b + 2*c*x^2)/(x^7*(b*x + c*x^3)^8),x]
[Out]
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Maple [B] time = 0.021, size = 197, normalized size = 10.9 \[ -{\frac{{c}^{8}}{2\,{b}^{13}} \left ( -{\frac{{b}^{6}}{7\,c \left ( c{x}^{2}+b \right ) ^{7}}}-66\,{\frac{b}{c \left ( c{x}^{2}+b \right ) ^{2}}}-{\frac{{b}^{5}}{c \left ( c{x}^{2}+b \right ) ^{6}}}-30\,{\frac{{b}^{2}}{c \left ( c{x}^{2}+b \right ) ^{3}}}-12\,{\frac{{b}^{3}}{c \left ( c{x}^{2}+b \right ) ^{4}}}-4\,{\frac{{b}^{4}}{c \left ( c{x}^{2}+b \right ) ^{5}}}-132\,{\frac{1}{ \left ( c{x}^{2}+b \right ) c}} \right ) }-{\frac{1}{14\,{b}^{7}{x}^{14}}}-66\,{\frac{{c}^{6}}{{b}^{13}{x}^{2}}}+33\,{\frac{{c}^{5}}{{b}^{12}{x}^{4}}}-15\,{\frac{{c}^{4}}{{b}^{11}{x}^{6}}}+6\,{\frac{{c}^{3}}{{b}^{10}{x}^{8}}}-2\,{\frac{{c}^{2}}{{b}^{9}{x}^{10}}}+{\frac{c}{2\,{b}^{8}{x}^{12}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*x^2+b)/x^7/(c*x^3+b*x)^8,x)
[Out]
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Maxima [A] time = 0.832899, size = 109, normalized size = 6.06 \[ -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)/((c*x^3 + b*x)^8*x^7),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.258191, size = 109, normalized size = 6.06 \[ -\frac{1}{14 \,{\left (c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)/((c*x^3 + b*x)^8*x^7),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**7/(c*x**3+b*x)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.264415, size = 20, normalized size = 1.11 \[ -\frac{1}{14 \,{\left (c x^{4} + b x^{2}\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x^2 + b)/((c*x^3 + b*x)^8*x^7),x, algorithm="giac")
[Out]