3.2586 \(\int x^{24} \left (a+b x^{25}\right )^{12} \, dx\)

Optimal. Leaf size=16 \[ \frac{\left (a+b x^{25}\right )^{13}}{325 b} \]

[Out]

(a + b*x^25)^13/(325*b)

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Rubi [A]  time = 0.0164596, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\left (a+b x^{25}\right )^{13}}{325 b} \]

Antiderivative was successfully verified.

[In]  Int[x^24*(a + b*x^25)^12,x]

[Out]

(a + b*x^25)^13/(325*b)

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Rubi in Sympy [A]  time = 2.15456, size = 10, normalized size = 0.62 \[ \frac{\left (a + b x^{25}\right )^{13}}{325 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**24*(b*x**25+a)**12,x)

[Out]

(a + b*x**25)**13/(325*b)

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Mathematica [B]  time = 0.00974764, size = 160, normalized size = 10. \[ \frac{a^{12} x^{25}}{25}+\frac{6}{25} a^{11} b x^{50}+\frac{22}{25} a^{10} b^2 x^{75}+\frac{11}{5} a^9 b^3 x^{100}+\frac{99}{25} a^8 b^4 x^{125}+\frac{132}{25} a^7 b^5 x^{150}+\frac{132}{25} a^6 b^6 x^{175}+\frac{99}{25} a^5 b^7 x^{200}+\frac{11}{5} a^4 b^8 x^{225}+\frac{22}{25} a^3 b^9 x^{250}+\frac{6}{25} a^2 b^{10} x^{275}+\frac{1}{25} a b^{11} x^{300}+\frac{b^{12} x^{325}}{325} \]

Antiderivative was successfully verified.

[In]  Integrate[x^24*(a + b*x^25)^12,x]

[Out]

(a^12*x^25)/25 + (6*a^11*b*x^50)/25 + (22*a^10*b^2*x^75)/25 + (11*a^9*b^3*x^100)
/5 + (99*a^8*b^4*x^125)/25 + (132*a^7*b^5*x^150)/25 + (132*a^6*b^6*x^175)/25 + (
99*a^5*b^7*x^200)/25 + (11*a^4*b^8*x^225)/5 + (22*a^3*b^9*x^250)/25 + (6*a^2*b^1
0*x^275)/25 + (a*b^11*x^300)/25 + (b^12*x^325)/325

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Maple [B]  time = 0.003, size = 135, normalized size = 8.4 \[{\frac{{b}^{12}{x}^{325}}{325}}+{\frac{a{b}^{11}{x}^{300}}{25}}+{\frac{6\,{a}^{2}{b}^{10}{x}^{275}}{25}}+{\frac{22\,{a}^{3}{b}^{9}{x}^{250}}{25}}+{\frac{11\,{b}^{8}{a}^{4}{x}^{225}}{5}}+{\frac{99\,{a}^{5}{b}^{7}{x}^{200}}{25}}+{\frac{132\,{a}^{6}{b}^{6}{x}^{175}}{25}}+{\frac{132\,{a}^{7}{b}^{5}{x}^{150}}{25}}+{\frac{99\,{a}^{8}{b}^{4}{x}^{125}}{25}}+{\frac{11\,{a}^{9}{b}^{3}{x}^{100}}{5}}+{\frac{22\,{a}^{10}{b}^{2}{x}^{75}}{25}}+{\frac{6\,{a}^{11}b{x}^{50}}{25}}+{\frac{{a}^{12}{x}^{25}}{25}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^24*(b*x^25+a)^12,x)

[Out]

1/325*b^12*x^325+1/25*a*b^11*x^300+6/25*a^2*b^10*x^275+22/25*a^3*b^9*x^250+11/5*
b^8*a^4*x^225+99/25*a^5*b^7*x^200+132/25*a^6*b^6*x^175+132/25*a^7*b^5*x^150+99/2
5*a^8*b^4*x^125+11/5*a^9*b^3*x^100+22/25*a^10*b^2*x^75+6/25*a^11*b*x^50+1/25*a^1
2*x^25

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Maxima [A]  time = 1.4211, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{25} + a\right )}^{13}}{325 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^25 + a)^12*x^24,x, algorithm="maxima")

[Out]

1/325*(b*x^25 + a)^13/b

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Fricas [A]  time = 0.181352, size = 1, normalized size = 0.06 \[ \frac{1}{325} x^{325} b^{12} + \frac{1}{25} x^{300} b^{11} a + \frac{6}{25} x^{275} b^{10} a^{2} + \frac{22}{25} x^{250} b^{9} a^{3} + \frac{11}{5} x^{225} b^{8} a^{4} + \frac{99}{25} x^{200} b^{7} a^{5} + \frac{132}{25} x^{175} b^{6} a^{6} + \frac{132}{25} x^{150} b^{5} a^{7} + \frac{99}{25} x^{125} b^{4} a^{8} + \frac{11}{5} x^{100} b^{3} a^{9} + \frac{22}{25} x^{75} b^{2} a^{10} + \frac{6}{25} x^{50} b a^{11} + \frac{1}{25} x^{25} a^{12} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^25 + a)^12*x^24,x, algorithm="fricas")

[Out]

1/325*x^325*b^12 + 1/25*x^300*b^11*a + 6/25*x^275*b^10*a^2 + 22/25*x^250*b^9*a^3
+ 11/5*x^225*b^8*a^4 + 99/25*x^200*b^7*a^5 + 132/25*x^175*b^6*a^6 + 132/25*x^15
0*b^5*a^7 + 99/25*x^125*b^4*a^8 + 11/5*x^100*b^3*a^9 + 22/25*x^75*b^2*a^10 + 6/2
5*x^50*b*a^11 + 1/25*x^25*a^12

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Sympy [A]  time = 0.231571, size = 160, normalized size = 10. \[ \frac{a^{12} x^{25}}{25} + \frac{6 a^{11} b x^{50}}{25} + \frac{22 a^{10} b^{2} x^{75}}{25} + \frac{11 a^{9} b^{3} x^{100}}{5} + \frac{99 a^{8} b^{4} x^{125}}{25} + \frac{132 a^{7} b^{5} x^{150}}{25} + \frac{132 a^{6} b^{6} x^{175}}{25} + \frac{99 a^{5} b^{7} x^{200}}{25} + \frac{11 a^{4} b^{8} x^{225}}{5} + \frac{22 a^{3} b^{9} x^{250}}{25} + \frac{6 a^{2} b^{10} x^{275}}{25} + \frac{a b^{11} x^{300}}{25} + \frac{b^{12} x^{325}}{325} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**24*(b*x**25+a)**12,x)

[Out]

a**12*x**25/25 + 6*a**11*b*x**50/25 + 22*a**10*b**2*x**75/25 + 11*a**9*b**3*x**1
00/5 + 99*a**8*b**4*x**125/25 + 132*a**7*b**5*x**150/25 + 132*a**6*b**6*x**175/2
5 + 99*a**5*b**7*x**200/25 + 11*a**4*b**8*x**225/5 + 22*a**3*b**9*x**250/25 + 6*
a**2*b**10*x**275/25 + a*b**11*x**300/25 + b**12*x**325/325

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GIAC/XCAS [A]  time = 0.214628, size = 19, normalized size = 1.19 \[ \frac{{\left (b x^{25} + a\right )}^{13}}{325 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x^25 + a)^12*x^24,x, algorithm="giac")

[Out]

1/325*(b*x^25 + a)^13/b