Optimal. Leaf size=15 \[ -\frac{1}{7 \left (b x+c x^2\right )^7} \]
[Out]
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Rubi [A] time = 0.00843283, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056 \[ -\frac{1}{7 \left (b x+c x^2\right )^7} \]
Antiderivative was successfully verified.
[In] Int[(b + 2*c*x)/(b*x + c*x^2)^8,x]
[Out]
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Rubi in Sympy [A] time = 3.18446, size = 14, normalized size = 0.93 \[ - \frac{1}{7 \left (b x + c x^{2}\right )^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2*c*x+b)/(c*x**2+b*x)**8,x)
[Out]
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Mathematica [A] time = 0.033947, size = 14, normalized size = 0.93 \[ -\frac{1}{7 x^7 (b+c x)^7} \]
Antiderivative was successfully verified.
[In] Integrate[(b + 2*c*x)/(b*x + c*x^2)^8,x]
[Out]
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Maple [B] time = 0.028, size = 177, normalized size = 11.8 \[ -{\frac{1}{7\,{b}^{7}{x}^{7}}}-132\,{\frac{{c}^{6}}{{b}^{13}x}}+66\,{\frac{{c}^{5}}{{b}^{12}{x}^{2}}}-30\,{\frac{{c}^{4}}{{b}^{11}{x}^{3}}}+12\,{\frac{{c}^{3}}{{b}^{10}{x}^{4}}}-4\,{\frac{{c}^{2}}{{b}^{9}{x}^{5}}}+{\frac{c}{{b}^{8}{x}^{6}}}+132\,{\frac{{c}^{7}}{{b}^{13} \left ( cx+b \right ) }}+66\,{\frac{{c}^{7}}{{b}^{12} \left ( cx+b \right ) ^{2}}}+30\,{\frac{{c}^{7}}{{b}^{11} \left ( cx+b \right ) ^{3}}}+12\,{\frac{{c}^{7}}{{b}^{10} \left ( cx+b \right ) ^{4}}}+4\,{\frac{{c}^{7}}{{b}^{9} \left ( cx+b \right ) ^{5}}}+{\frac{{c}^{7}}{{b}^{8} \left ( cx+b \right ) ^{6}}}+{\frac{{c}^{7}}{7\,{b}^{7} \left ( cx+b \right ) ^{7}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2*c*x+b)/(c*x^2+b*x)^8,x)
[Out]
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Maxima [A] time = 0.745359, size = 18, normalized size = 1.2 \[ -\frac{1}{7 \,{\left (c x^{2} + b x\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x)^8,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.259154, size = 109, normalized size = 7.27 \[ -\frac{1}{7 \,{\left (c^{7} x^{14} + 7 \, b c^{6} x^{13} + 21 \, b^{2} c^{5} x^{12} + 35 \, b^{3} c^{4} x^{11} + 35 \, b^{4} c^{3} x^{10} + 21 \, b^{5} c^{2} x^{9} + 7 \, b^{6} c x^{8} + b^{7} x^{7}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x)^8,x, algorithm="fricas")
[Out]
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Sympy [A] time = 17.6276, size = 87, normalized size = 5.8 \[ - \frac{1}{7 b^{7} x^{7} + 49 b^{6} c x^{8} + 147 b^{5} c^{2} x^{9} + 245 b^{4} c^{3} x^{10} + 245 b^{3} c^{4} x^{11} + 147 b^{2} c^{5} x^{12} + 49 b c^{6} x^{13} + 7 c^{7} x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x+b)/(c*x**2+b*x)**8,x)
[Out]
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GIAC/XCAS [A] time = 0.267178, size = 18, normalized size = 1.2 \[ -\frac{1}{7 \,{\left (c x^{2} + b x\right )}^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)/(c*x^2 + b*x)^8,x, algorithm="giac")
[Out]