Optimal. Leaf size=21 \[ \frac{\left (a x+b x^{38}\right )^{13}}{481 b x^{13}} \]
[Out]
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Rubi [A] time = 0.0123021, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ \frac{\left (a x+b x^{38}\right )^{13}}{481 b x^{13}} \]
Antiderivative was successfully verified.
[In] Int[x^24*(a*x + b*x^38)^12,x]
[Out]
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Rubi in Sympy [A] time = 3.29027, size = 10, normalized size = 0.48 \[ \frac{\left (a + b x^{37}\right )^{13}}{481 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**24*(b*x**38+a*x)**12,x)
[Out]
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Mathematica [B] time = 0.0103694, size = 160, normalized size = 7.62 \[ \frac{a^{12} x^{37}}{37}+\frac{6}{37} a^{11} b x^{74}+\frac{22}{37} a^{10} b^2 x^{111}+\frac{55}{37} a^9 b^3 x^{148}+\frac{99}{37} a^8 b^4 x^{185}+\frac{132}{37} a^7 b^5 x^{222}+\frac{132}{37} a^6 b^6 x^{259}+\frac{99}{37} a^5 b^7 x^{296}+\frac{55}{37} a^4 b^8 x^{333}+\frac{22}{37} a^3 b^9 x^{370}+\frac{6}{37} a^2 b^{10} x^{407}+\frac{1}{37} a b^{11} x^{444}+\frac{b^{12} x^{481}}{481} \]
Antiderivative was successfully verified.
[In] Integrate[x^24*(a*x + b*x^38)^12,x]
[Out]
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Maple [B] time = 0., size = 135, normalized size = 6.4 \[{\frac{{b}^{12}{x}^{481}}{481}}+{\frac{a{b}^{11}{x}^{444}}{37}}+{\frac{6\,{a}^{2}{b}^{10}{x}^{407}}{37}}+{\frac{22\,{a}^{3}{b}^{9}{x}^{370}}{37}}+{\frac{55\,{b}^{8}{a}^{4}{x}^{333}}{37}}+{\frac{99\,{a}^{5}{b}^{7}{x}^{296}}{37}}+{\frac{132\,{a}^{6}{b}^{6}{x}^{259}}{37}}+{\frac{132\,{a}^{7}{b}^{5}{x}^{222}}{37}}+{\frac{99\,{a}^{8}{b}^{4}{x}^{185}}{37}}+{\frac{55\,{a}^{9}{b}^{3}{x}^{148}}{37}}+{\frac{22\,{a}^{10}{b}^{2}{x}^{111}}{37}}+{\frac{6\,{a}^{11}b{x}^{74}}{37}}+{\frac{{a}^{12}{x}^{37}}{37}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^24*(b*x^38+a*x)^12,x)
[Out]
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Maxima [A] time = 1.3749, size = 181, normalized size = 8.62 \[ \frac{1}{481} \, b^{12} x^{481} + \frac{1}{37} \, a b^{11} x^{444} + \frac{6}{37} \, a^{2} b^{10} x^{407} + \frac{22}{37} \, a^{3} b^{9} x^{370} + \frac{55}{37} \, a^{4} b^{8} x^{333} + \frac{99}{37} \, a^{5} b^{7} x^{296} + \frac{132}{37} \, a^{6} b^{6} x^{259} + \frac{132}{37} \, a^{7} b^{5} x^{222} + \frac{99}{37} \, a^{8} b^{4} x^{185} + \frac{55}{37} \, a^{9} b^{3} x^{148} + \frac{22}{37} \, a^{10} b^{2} x^{111} + \frac{6}{37} \, a^{11} b x^{74} + \frac{1}{37} \, a^{12} x^{37} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^38 + a*x)^12*x^24,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.199328, size = 1, normalized size = 0.05 \[ \frac{1}{481} x^{481} b^{12} + \frac{1}{37} x^{444} b^{11} a + \frac{6}{37} x^{407} b^{10} a^{2} + \frac{22}{37} x^{370} b^{9} a^{3} + \frac{55}{37} x^{333} b^{8} a^{4} + \frac{99}{37} x^{296} b^{7} a^{5} + \frac{132}{37} x^{259} b^{6} a^{6} + \frac{132}{37} x^{222} b^{5} a^{7} + \frac{99}{37} x^{185} b^{4} a^{8} + \frac{55}{37} x^{148} b^{3} a^{9} + \frac{22}{37} x^{111} b^{2} a^{10} + \frac{6}{37} x^{74} b a^{11} + \frac{1}{37} x^{37} a^{12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^38 + a*x)^12*x^24,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.287666, size = 160, normalized size = 7.62 \[ \frac{a^{12} x^{37}}{37} + \frac{6 a^{11} b x^{74}}{37} + \frac{22 a^{10} b^{2} x^{111}}{37} + \frac{55 a^{9} b^{3} x^{148}}{37} + \frac{99 a^{8} b^{4} x^{185}}{37} + \frac{132 a^{7} b^{5} x^{222}}{37} + \frac{132 a^{6} b^{6} x^{259}}{37} + \frac{99 a^{5} b^{7} x^{296}}{37} + \frac{55 a^{4} b^{8} x^{333}}{37} + \frac{22 a^{3} b^{9} x^{370}}{37} + \frac{6 a^{2} b^{10} x^{407}}{37} + \frac{a b^{11} x^{444}}{37} + \frac{b^{12} x^{481}}{481} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**24*(b*x**38+a*x)**12,x)
[Out]
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GIAC/XCAS [A] time = 0.221089, size = 181, normalized size = 8.62 \[ \frac{1}{481} \, b^{12} x^{481} + \frac{1}{37} \, a b^{11} x^{444} + \frac{6}{37} \, a^{2} b^{10} x^{407} + \frac{22}{37} \, a^{3} b^{9} x^{370} + \frac{55}{37} \, a^{4} b^{8} x^{333} + \frac{99}{37} \, a^{5} b^{7} x^{296} + \frac{132}{37} \, a^{6} b^{6} x^{259} + \frac{132}{37} \, a^{7} b^{5} x^{222} + \frac{99}{37} \, a^{8} b^{4} x^{185} + \frac{55}{37} \, a^{9} b^{3} x^{148} + \frac{22}{37} \, a^{10} b^{2} x^{111} + \frac{6}{37} \, a^{11} b x^{74} + \frac{1}{37} \, a^{12} x^{37} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x^38 + a*x)^12*x^24,x, algorithm="giac")
[Out]