Optimal. Leaf size=54 \[ -\frac{a^2 x^3}{9}-\frac{b^3 \log (x)}{3 a}-\frac{1}{2} a b x^2+\frac{\log (x) (a x+b)^3}{3 a}-b^2 x \]
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Rubi [A] time = 0.0522001, antiderivative size = 54, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4 \[ -\frac{a^2 x^3}{9}-\frac{b^3 \log (x)}{3 a}-\frac{1}{2} a b x^2+\frac{\log (x) (a x+b)^3}{3 a}-b^2 x \]
Antiderivative was successfully verified.
[In] Int[(b + a*x)^2*Log[x],x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{a^{2} x^{3}}{9} - a b \int x\, dx - b^{2} x - \frac{b^{3} \log{\left (x \right )}}{3 a} + \frac{\left (a x + b\right )^{3} \log{\left (x \right )}}{3 a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a*x+b)**2*ln(x),x)
[Out]
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Mathematica [A] time = 0.0143132, size = 46, normalized size = 0.85 \[ \frac{1}{18} x \left (6 \log (x) \left (a^2 x^2+3 a b x+3 b^2\right )-2 a^2 x^2-9 a b x-18 b^2\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(b + a*x)^2*Log[x],x]
[Out]
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Maple [A] time = 0.001, size = 48, normalized size = 0.9 \[{\frac{{a}^{2}{x}^{3}\ln \left ( x \right ) }{3}}-{\frac{{a}^{2}{x}^{3}}{9}}+ab{x}^{2}\ln \left ( x \right ) -{\frac{ab{x}^{2}}{2}}+\ln \left ( x \right ) x{b}^{2}-{b}^{2}x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a*x+b)^2*ln(x),x)
[Out]
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Maxima [A] time = 1.42692, size = 63, normalized size = 1.17 \[ -\frac{1}{9} \, a^{2} x^{3} - \frac{1}{2} \, a b x^{2} - b^{2} x + \frac{1}{3} \,{\left (a^{2} x^{3} + 3 \, a b x^{2} + 3 \, b^{2} x\right )} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b)^2*log(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.204077, size = 63, normalized size = 1.17 \[ -\frac{1}{9} \, a^{2} x^{3} - \frac{1}{2} \, a b x^{2} - b^{2} x + \frac{1}{3} \,{\left (a^{2} x^{3} + 3 \, a b x^{2} + 3 \, b^{2} x\right )} \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b)^2*log(x),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.132458, size = 44, normalized size = 0.81 \[ - \frac{a^{2} x^{3}}{9} - \frac{a b x^{2}}{2} - b^{2} x + \left (\frac{a^{2} x^{3}}{3} + a b x^{2} + b^{2} x\right ) \log{\left (x \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x+b)**2*ln(x),x)
[Out]
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GIAC/XCAS [A] time = 0.199139, size = 63, normalized size = 1.17 \[ \frac{1}{3} \, a^{2} x^{3}{\rm ln}\left (x\right ) - \frac{1}{9} \, a^{2} x^{3} + a b x^{2}{\rm ln}\left (x\right ) - \frac{1}{2} \, a b x^{2} + b^{2} x{\rm ln}\left (x\right ) - b^{2} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a*x + b)^2*log(x),x, algorithm="giac")
[Out]