Optimal. Leaf size=14 \[ \frac{(a+b x)^6}{6 b} \]
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Rubi [B] time = 0.0343188, antiderivative size = 61, normalized size of antiderivative = 4.36, number of steps used = 1, number of rules used = 0, integrand size = 49, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a^5 x+\frac{5}{2} a^4 b x^2+\frac{10}{3} a^3 b^2 x^3+\frac{5}{2} a^2 b^3 x^4+a b^4 x^5+\frac{b^5 x^6}{6} \]
Antiderivative was successfully verified.
[In] Int[a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5,x]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ 5 a^{4} b \int x\, dx + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6} + \int a^{5}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(b**5*x**5+5*a*b**4*x**4+10*a**2*b**3*x**3+10*a**3*b**2*x**2+5*a**4*b*x+a**5,x)
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Mathematica [B] time = 0.0000892753, size = 61, normalized size = 4.36 \[ a^5 x+\frac{5}{2} a^4 b x^2+\frac{10}{3} a^3 b^2 x^3+\frac{5}{2} a^2 b^3 x^4+a b^4 x^5+\frac{b^5 x^6}{6} \]
Antiderivative was successfully verified.
[In] Integrate[a^5 + 5*a^4*b*x + 10*a^3*b^2*x^2 + 10*a^2*b^3*x^3 + 5*a*b^4*x^4 + b^5*x^5,x]
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Maple [B] time = 0.001, size = 54, normalized size = 3.9 \[{a}^{5}x+{\frac{5\,{a}^{4}b{x}^{2}}{2}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{3}}{3}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{4}}{2}}+a{b}^{4}{x}^{5}+{\frac{{b}^{5}{x}^{6}}{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(b^5*x^5+5*a*b^4*x^4+10*a^2*b^3*x^3+10*a^3*b^2*x^2+5*a^4*b*x+a^5,x)
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Maxima [A] time = 0.795292, size = 72, normalized size = 5.14 \[ \frac{1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^5*x^5 + 5*a*b^4*x^4 + 10*a^2*b^3*x^3 + 10*a^3*b^2*x^2 + 5*a^4*b*x + a^5,x, algorithm="maxima")
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Fricas [A] time = 0.23727, size = 1, normalized size = 0.07 \[ \frac{1}{6} x^{6} b^{5} + x^{5} b^{4} a + \frac{5}{2} x^{4} b^{3} a^{2} + \frac{10}{3} x^{3} b^{2} a^{3} + \frac{5}{2} x^{2} b a^{4} + x a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^5*x^5 + 5*a*b^4*x^4 + 10*a^2*b^3*x^3 + 10*a^3*b^2*x^2 + 5*a^4*b*x + a^5,x, algorithm="fricas")
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Sympy [A] time = 0.105178, size = 60, normalized size = 4.29 \[ a^{5} x + \frac{5 a^{4} b x^{2}}{2} + \frac{10 a^{3} b^{2} x^{3}}{3} + \frac{5 a^{2} b^{3} x^{4}}{2} + a b^{4} x^{5} + \frac{b^{5} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b**5*x**5+5*a*b**4*x**4+10*a**2*b**3*x**3+10*a**3*b**2*x**2+5*a**4*b*x+a**5,x)
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GIAC/XCAS [A] time = 0.25914, size = 72, normalized size = 5.14 \[ \frac{1}{6} \, b^{5} x^{6} + a b^{4} x^{5} + \frac{5}{2} \, a^{2} b^{3} x^{4} + \frac{10}{3} \, a^{3} b^{2} x^{3} + \frac{5}{2} \, a^{4} b x^{2} + a^{5} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(b^5*x^5 + 5*a*b^4*x^4 + 10*a^2*b^3*x^3 + 10*a^3*b^2*x^2 + 5*a^4*b*x + a^5,x, algorithm="giac")
[Out]