Optimal. Leaf size=14 \[ \frac{(a+b x)^3}{3 b} \]
[Out]
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Rubi [A] time = 0.00701627, 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 \[ \frac{(a+b x)^3}{3 b} \]
Antiderivative was successfully verified.
[In] Int[(a + b*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 1.28959, size = 8, normalized size = 0.57 \[ \frac{\left (a + b x\right )^{3}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**2,x)
[Out]
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Mathematica [A] time = 0.00143096, size = 14, normalized size = 1. \[ \frac{(a+b x)^3}{3 b} \]
Antiderivative was successfully verified.
[In] Integrate[(a + b*x)^2,x]
[Out]
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Maple [A] time = 0., size = 13, normalized size = 0.9 \[{\frac{ \left ( bx+a \right ) ^{3}}{3\,b}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^2,x)
[Out]
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Maxima [A] time = 1.34964, size = 27, normalized size = 1.93 \[ \frac{1}{3} \, b^{2} x^{3} + a b x^{2} + a^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.194881, size = 1, normalized size = 0.07 \[ \frac{1}{3} x^{3} b^{2} + x^{2} b a + x a^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.080035, size = 19, normalized size = 1.36 \[ a^{2} x + a b x^{2} + \frac{b^{2} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.204439, size = 16, normalized size = 1.14 \[ \frac{{\left (b x + a\right )}^{3}}{3 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x + a)^2,x, algorithm="giac")
[Out]