Optimal. Leaf size=21 \[ \frac{x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
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Rubi [A] time = 0.0616745, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.103 \[ \frac{x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
Antiderivative was successfully verified.
[In] Int[x^(-1 + n)*(b + 2*c*x^n)*(b*x^n + c*x^(2*n))^13,x]
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Rubi in Sympy [A] time = 12.011, size = 15, normalized size = 0.71 \[ \frac{x^{14 n} \left (b + c x^{n}\right )^{14}}{14 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(-1+n)*(b+2*c*x**n)*(b*x**n+c*x**(2*n))**13,x)
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Mathematica [A] time = 0.0541722, size = 21, normalized size = 1. \[ \frac{x^{14 n} \left (b+c x^n\right )^{14}}{14 n} \]
Antiderivative was successfully verified.
[In] Integrate[x^(-1 + n)*(b + 2*c*x^n)*(b*x^n + c*x^(2*n))^13,x]
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Maple [B] time = 0.057, size = 230, normalized size = 11. \[{\frac{{c}^{14} \left ({x}^{n} \right ) ^{28}}{14\,n}}+{\frac{b{c}^{13} \left ({x}^{n} \right ) ^{27}}{n}}+{\frac{13\,{c}^{12} \left ({x}^{n} \right ) ^{26}{b}^{2}}{2\,n}}+26\,{\frac{{b}^{3}{c}^{11} \left ({x}^{n} \right ) ^{25}}{n}}+{\frac{143\,{c}^{10} \left ({x}^{n} \right ) ^{24}{b}^{4}}{2\,n}}+143\,{\frac{{b}^{5}{c}^{9} \left ({x}^{n} \right ) ^{23}}{n}}+{\frac{429\,{c}^{8} \left ({x}^{n} \right ) ^{22}{b}^{6}}{2\,n}}+{\frac{1716\,{b}^{7}{c}^{7} \left ({x}^{n} \right ) ^{21}}{7\,n}}+{\frac{429\,{c}^{6} \left ({x}^{n} \right ) ^{20}{b}^{8}}{2\,n}}+143\,{\frac{{b}^{9}{c}^{5} \left ({x}^{n} \right ) ^{19}}{n}}+{\frac{143\,{c}^{4} \left ({x}^{n} \right ) ^{18}{b}^{10}}{2\,n}}+26\,{\frac{{b}^{11}{c}^{3} \left ({x}^{n} \right ) ^{17}}{n}}+{\frac{13\,{c}^{2} \left ({x}^{n} \right ) ^{16}{b}^{12}}{2\,n}}+{\frac{{b}^{13}c \left ({x}^{n} \right ) ^{15}}{n}}+{\frac{ \left ({x}^{n} \right ) ^{14}{b}^{14}}{14\,n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(-1+n)*(b+2*c*x^n)*(b*x^n+c*x^(2*n))^13,x)
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^(2*n) + b*x^n)^13*(2*c*x^n + b)*x^(n - 1),x, algorithm="maxima")
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Fricas [A] time = 0.316339, size = 255, normalized size = 12.14 \[ \frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^(2*n) + b*x^n)^13*(2*c*x^n + b)*x^(n - 1),x, algorithm="fricas")
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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(x**(-1+n)*(b+2*c*x**n)*(b*x**n+c*x**(2*n))**13,x)
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GIAC/XCAS [A] time = 0.270288, size = 255, normalized size = 12.14 \[ \frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^(2*n) + b*x^n)^13*(2*c*x^n + b)*x^(n - 1),x, algorithm="giac")
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