Optimal. Leaf size=27 \[ \frac{\left (a+b x^{12 m+1}\right )^{13}}{13 b (12 m+1)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0229146, antiderivative size = 27, 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 \[ \frac{\left (a+b x^{12 m+1}\right )^{13}}{13 b (12 m+1)} \]
Antiderivative was successfully verified.
[In] Int[x^(12 + 12*(-1 + m))*(a + b*x^(1 + 12*m))^12,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.72144, size = 19, normalized size = 0.7 \[ \frac{\left (a + b x^{12 m + 1}\right )^{13}}{13 b \left (12 m + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**(12*m)*(a+b*x**(1+12*m))**12,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0104215, size = 24, normalized size = 0.89 \[ \frac{\left (a+b x^{12 m+1}\right )^{13}}{156 b m+13 b} \]
Antiderivative was successfully verified.
[In] Integrate[x^(12 + 12*(-1 + m))*(a + b*x^(1 + 12*m))^12,x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0., size = 311, normalized size = 11.5 \[{\frac{{b}^{12}{x}^{13} \left ({x}^{12\,m} \right ) ^{13}}{13+156\,m}}+{\frac{a{b}^{11}{x}^{12} \left ({x}^{12\,m} \right ) ^{12}}{1+12\,m}}+6\,{\frac{{a}^{2}{b}^{10}{x}^{11} \left ({x}^{12\,m} \right ) ^{11}}{1+12\,m}}+22\,{\frac{{a}^{3}{b}^{9}{x}^{10} \left ({x}^{12\,m} \right ) ^{10}}{1+12\,m}}+55\,{\frac{{a}^{4}{b}^{8}{x}^{9} \left ({x}^{12\,m} \right ) ^{9}}{1+12\,m}}+99\,{\frac{{a}^{5}{b}^{7}{x}^{8} \left ({x}^{12\,m} \right ) ^{8}}{1+12\,m}}+132\,{\frac{{a}^{6}{b}^{6}{x}^{7} \left ({x}^{12\,m} \right ) ^{7}}{1+12\,m}}+132\,{\frac{{a}^{7}{b}^{5}{x}^{6} \left ({x}^{12\,m} \right ) ^{6}}{1+12\,m}}+99\,{\frac{{a}^{8}{b}^{4}{x}^{5} \left ({x}^{12\,m} \right ) ^{5}}{1+12\,m}}+55\,{\frac{{a}^{9}{b}^{3}{x}^{4} \left ({x}^{12\,m} \right ) ^{4}}{1+12\,m}}+22\,{\frac{{a}^{10}{b}^{2}{x}^{3} \left ({x}^{12\,m} \right ) ^{3}}{1+12\,m}}+6\,{\frac{{a}^{11}b{x}^{2} \left ({x}^{12\,m} \right ) ^{2}}{1+12\,m}}+{\frac{{a}^{12}x{x}^{12\,m}}{1+12\,m}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^(12*m)*(a+b*x^(1+12*m))^12,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.43444, size = 34, normalized size = 1.26 \[ \frac{{\left (b x^{12 \, m + 1} + a\right )}^{13}}{13 \, b{\left (12 \, m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(12*m + 1) + a)^12*x^(12*m),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.227371, size = 262, normalized size = 9.7 \[ \frac{b^{12} x^{156 \, m + 13} + 13 \, a b^{11} x^{144 \, m + 12} + 78 \, a^{2} b^{10} x^{132 \, m + 11} + 286 \, a^{3} b^{9} x^{120 \, m + 10} + 715 \, a^{4} b^{8} x^{108 \, m + 9} + 1287 \, a^{5} b^{7} x^{96 \, m + 8} + 1716 \, a^{6} b^{6} x^{84 \, m + 7} + 1716 \, a^{7} b^{5} x^{72 \, m + 6} + 1287 \, a^{8} b^{4} x^{60 \, m + 5} + 715 \, a^{9} b^{3} x^{48 \, m + 4} + 286 \, a^{10} b^{2} x^{36 \, m + 3} + 78 \, a^{11} b x^{24 \, m + 2} + 13 \, a^{12} x^{12 \, m + 1}}{13 \,{\left (12 \, m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(12*m + 1) + a)^12*x^(12*m),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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**(12*m)*(a+b*x**(1+12*m))**12,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.241854, size = 294, normalized size = 10.89 \[ \frac{b^{12} x^{13} e^{\left (156 \, m{\rm ln}\left (x\right )\right )} + 13 \, a b^{11} x^{12} e^{\left (144 \, m{\rm ln}\left (x\right )\right )} + 78 \, a^{2} b^{10} x^{11} e^{\left (132 \, m{\rm ln}\left (x\right )\right )} + 286 \, a^{3} b^{9} x^{10} e^{\left (120 \, m{\rm ln}\left (x\right )\right )} + 715 \, a^{4} b^{8} x^{9} e^{\left (108 \, m{\rm ln}\left (x\right )\right )} + 1287 \, a^{5} b^{7} x^{8} e^{\left (96 \, m{\rm ln}\left (x\right )\right )} + 1716 \, a^{6} b^{6} x^{7} e^{\left (84 \, m{\rm ln}\left (x\right )\right )} + 1716 \, a^{7} b^{5} x^{6} e^{\left (72 \, m{\rm ln}\left (x\right )\right )} + 1287 \, a^{8} b^{4} x^{5} e^{\left (60 \, m{\rm ln}\left (x\right )\right )} + 715 \, a^{9} b^{3} x^{4} e^{\left (48 \, m{\rm ln}\left (x\right )\right )} + 286 \, a^{10} b^{2} x^{3} e^{\left (36 \, m{\rm ln}\left (x\right )\right )} + 78 \, a^{11} b x^{2} e^{\left (24 \, m{\rm ln}\left (x\right )\right )} + 13 \, a^{12} x e^{\left (12 \, m{\rm ln}\left (x\right )\right )}}{13 \,{\left (12 \, m + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^(12*m + 1) + a)^12*x^(12*m),x, algorithm="giac")
[Out]