Optimal. Leaf size=17 \[ a c x+\frac{1}{2} x^2 (b c+d) \]
[Out]
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Rubi [A] time = 0.0192166, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 0, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ a c x+\frac{1}{2} x^2 (b c+d) \]
Antiderivative was successfully verified.
[In] Int[a*c + (b*c + d)*x,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ c \int a\, dx + \left (b c + d\right ) \int x\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(a*c+(b*c+d)*x,x)
[Out]
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Mathematica [A] time = 0.0000479975, size = 22, normalized size = 1.29 \[ a c x+\frac{1}{2} b c x^2+\frac{d x^2}{2} \]
Antiderivative was successfully verified.
[In] Integrate[a*c + (b*c + d)*x,x]
[Out]
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Maple [A] time = 0.001, size = 16, normalized size = 0.9 \[ acx+{\frac{ \left ( bc+d \right ){x}^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(a*c+(b*c+d)*x,x)
[Out]
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Maxima [A] time = 0.78335, size = 20, normalized size = 1.18 \[ a c x + \frac{1}{2} \,{\left (b c + d\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a*c + (b*c + d)*x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247731, size = 1, normalized size = 0.06 \[ \frac{1}{2} x^{2} c b + \frac{1}{2} x^{2} d + x c a \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a*c + (b*c + d)*x,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.069167, size = 15, normalized size = 0.88 \[ a c x + x^{2} \left (\frac{b c}{2} + \frac{d}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a*c+(b*c+d)*x,x)
[Out]
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GIAC/XCAS [A] time = 0.257955, size = 20, normalized size = 1.18 \[ a c x + \frac{1}{2} \,{\left (b c + d\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a*c + (b*c + d)*x,x, algorithm="giac")
[Out]