Optimal. Leaf size=14 \[ \frac{1}{14} x^{14} (b+c x)^{14} \]
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Rubi [A] time = 0.016969, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{1}{14} x^{14} (b+c x)^{14} \]
Antiderivative was successfully verified.
[In] Int[x^13*(b + c*x)^13*(b + 2*c*x),x]
[Out]
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Rubi in Sympy [A] time = 4.37269, size = 10, normalized size = 0.71 \[ \frac{x^{14} \left (b + c x\right )^{14}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**13*(c*x+b)**13*(2*c*x+b),x)
[Out]
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Mathematica [B] time = 0.00902768, size = 172, normalized size = 12.29 \[ \frac{b^{14} x^{14}}{14}+b^{13} c x^{15}+\frac{13}{2} b^{12} c^2 x^{16}+26 b^{11} c^3 x^{17}+\frac{143}{2} b^{10} c^4 x^{18}+143 b^9 c^5 x^{19}+\frac{429}{2} b^8 c^6 x^{20}+\frac{1716}{7} b^7 c^7 x^{21}+\frac{429}{2} b^6 c^8 x^{22}+143 b^5 c^9 x^{23}+\frac{143}{2} b^4 c^{10} x^{24}+26 b^3 c^{11} x^{25}+\frac{13}{2} b^2 c^{12} x^{26}+b c^{13} x^{27}+\frac{c^{14} x^{28}}{14} \]
Antiderivative was successfully verified.
[In] Integrate[x^13*(b + c*x)^13*(b + 2*c*x),x]
[Out]
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Maple [B] time = 0.004, size = 155, normalized size = 11.1 \[{\frac{{c}^{14}{x}^{28}}{14}}+b{c}^{13}{x}^{27}+{\frac{13\,{b}^{2}{c}^{12}{x}^{26}}{2}}+26\,{b}^{3}{c}^{11}{x}^{25}+{\frac{143\,{b}^{4}{c}^{10}{x}^{24}}{2}}+143\,{b}^{5}{c}^{9}{x}^{23}+{\frac{429\,{b}^{6}{c}^{8}{x}^{22}}{2}}+{\frac{1716\,{b}^{7}{c}^{7}{x}^{21}}{7}}+{\frac{429\,{b}^{8}{c}^{6}{x}^{20}}{2}}+143\,{b}^{9}{c}^{5}{x}^{19}+{\frac{143\,{b}^{10}{c}^{4}{x}^{18}}{2}}+26\,{b}^{11}{c}^{3}{x}^{17}+{\frac{13\,{b}^{12}{c}^{2}{x}^{16}}{2}}+{b}^{13}c{x}^{15}+{\frac{{b}^{14}{x}^{14}}{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^13*(c*x+b)^13*(2*c*x+b),x)
[Out]
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Maxima [A] time = 1.36941, size = 208, normalized size = 14.86 \[ \frac{1}{14} \, c^{14} x^{28} + b c^{13} x^{27} + \frac{13}{2} \, b^{2} c^{12} x^{26} + 26 \, b^{3} c^{11} x^{25} + \frac{143}{2} \, b^{4} c^{10} x^{24} + 143 \, b^{5} c^{9} x^{23} + \frac{429}{2} \, b^{6} c^{8} x^{22} + \frac{1716}{7} \, b^{7} c^{7} x^{21} + \frac{429}{2} \, b^{8} c^{6} x^{20} + 143 \, b^{9} c^{5} x^{19} + \frac{143}{2} \, b^{10} c^{4} x^{18} + 26 \, b^{11} c^{3} x^{17} + \frac{13}{2} \, b^{12} c^{2} x^{16} + b^{13} c x^{15} + \frac{1}{14} \, b^{14} x^{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*(c*x + b)^13*x^13,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.185686, size = 1, normalized size = 0.07 \[ \frac{1}{14} x^{28} c^{14} + x^{27} c^{13} b + \frac{13}{2} x^{26} c^{12} b^{2} + 26 x^{25} c^{11} b^{3} + \frac{143}{2} x^{24} c^{10} b^{4} + 143 x^{23} c^{9} b^{5} + \frac{429}{2} x^{22} c^{8} b^{6} + \frac{1716}{7} x^{21} c^{7} b^{7} + \frac{429}{2} x^{20} c^{6} b^{8} + 143 x^{19} c^{5} b^{9} + \frac{143}{2} x^{18} c^{4} b^{10} + 26 x^{17} c^{3} b^{11} + \frac{13}{2} x^{16} c^{2} b^{12} + x^{15} c b^{13} + \frac{1}{14} x^{14} b^{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*(c*x + b)^13*x^13,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.1213, size = 175, normalized size = 12.5 \[ \frac{b^{14} x^{14}}{14} + b^{13} c x^{15} + \frac{13 b^{12} c^{2} x^{16}}{2} + 26 b^{11} c^{3} x^{17} + \frac{143 b^{10} c^{4} x^{18}}{2} + 143 b^{9} c^{5} x^{19} + \frac{429 b^{8} c^{6} x^{20}}{2} + \frac{1716 b^{7} c^{7} x^{21}}{7} + \frac{429 b^{6} c^{8} x^{22}}{2} + 143 b^{5} c^{9} x^{23} + \frac{143 b^{4} c^{10} x^{24}}{2} + 26 b^{3} c^{11} x^{25} + \frac{13 b^{2} c^{12} x^{26}}{2} + b c^{13} x^{27} + \frac{c^{14} x^{28}}{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**13*(c*x+b)**13*(2*c*x+b),x)
[Out]
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GIAC/XCAS [A] time = 0.208466, size = 208, normalized size = 14.86 \[ \frac{1}{14} \, c^{14} x^{28} + b c^{13} x^{27} + \frac{13}{2} \, b^{2} c^{12} x^{26} + 26 \, b^{3} c^{11} x^{25} + \frac{143}{2} \, b^{4} c^{10} x^{24} + 143 \, b^{5} c^{9} x^{23} + \frac{429}{2} \, b^{6} c^{8} x^{22} + \frac{1716}{7} \, b^{7} c^{7} x^{21} + \frac{429}{2} \, b^{8} c^{6} x^{20} + 143 \, b^{9} c^{5} x^{19} + \frac{143}{2} \, b^{10} c^{4} x^{18} + 26 \, b^{11} c^{3} x^{17} + \frac{13}{2} \, b^{12} c^{2} x^{16} + b^{13} c x^{15} + \frac{1}{14} \, b^{14} x^{14} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2*c*x + b)*(c*x + b)^13*x^13,x, algorithm="giac")
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