Optimal. Leaf size=14 \[ \frac{(a+b x)^8}{8 b} \]
[Out]
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Rubi [A] time = 0.00692603, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{(a+b x)^8}{8 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^7,x]
[Out]
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Rubi in Sympy [A] time = 1.27103, size = 8, normalized size = 0.57 \[ \frac{\left (a + b x\right )^{8}}{8 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**7,x)
[Out]
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Mathematica [A] time = 0.00120698, size = 14, normalized size = 1. \[ \frac{(a+b x)^8}{8 b} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^7,x]
[Out]
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Maple [A] time = 0., size = 13, normalized size = 0.9 \[{\frac{ \left ( bx+a \right ) ^{8}}{8\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^7,x)
[Out]
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Maxima [A] time = 1.33965, size = 16, normalized size = 1.14 \[ \frac{{\left (b x + a\right )}^{8}}{8 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.187577, size = 1, normalized size = 0.07 \[ \frac{1}{8} x^{8} b^{7} + x^{7} b^{6} a + \frac{7}{2} x^{6} b^{5} a^{2} + 7 x^{5} b^{4} a^{3} + \frac{35}{4} x^{4} b^{3} a^{4} + 7 x^{3} b^{2} a^{5} + \frac{7}{2} x^{2} b a^{6} + x a^{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.141681, size = 83, normalized size = 5.93 \[ a^{7} x + \frac{7 a^{6} b x^{2}}{2} + 7 a^{5} b^{2} x^{3} + \frac{35 a^{4} b^{3} x^{4}}{4} + 7 a^{3} b^{4} x^{5} + \frac{7 a^{2} b^{5} x^{6}}{2} + a b^{6} x^{7} + \frac{b^{7} x^{8}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**7,x)
[Out]
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GIAC/XCAS [A] time = 0.210359, size = 16, normalized size = 1.14 \[ \frac{{\left (b x + a\right )}^{8}}{8 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^7,x, algorithm="giac")
[Out]