Optimal. Leaf size=28 \[ \frac{x^{n+1} \log (a x)}{n+1}-\frac{x^{n+1}}{(n+1)^2} \]
[Out]
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Rubi [A] time = 0.0199525, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{x^{n+1} \log (a x)}{n+1}-\frac{x^{n+1}}{(n+1)^2} \]
Antiderivative was successfully verified.
[In] Int[x^n*Log[a*x],x]
[Out]
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Rubi in Sympy [A] time = 1.61621, size = 22, normalized size = 0.79 \[ \frac{x^{n + 1} \log{\left (a x \right )}}{n + 1} - \frac{x^{n + 1}}{\left (n + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**n*ln(a*x),x)
[Out]
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Mathematica [A] time = 0.0141084, size = 21, normalized size = 0.75 \[ \frac{x^{n+1} ((n+1) \log (a x)-1)}{(n+1)^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^n*Log[a*x],x]
[Out]
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Maple [A] time = 0.083, size = 36, normalized size = 1.3 \[{\frac{x\ln \left ( ax \right ){{\rm e}^{n\ln \left ( x \right ) }}}{1+n}}-{\frac{x{{\rm e}^{n\ln \left ( x \right ) }}}{{n}^{2}+2\,n+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^n*ln(a*x),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^n*log(a*x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218856, size = 43, normalized size = 1.54 \[ \frac{{\left ({\left (n + 1\right )} x \log \left (a\right ) +{\left (n + 1\right )} x \log \left (x\right ) - x\right )} x^{n}}{n^{2} + 2 \, n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^n*log(a*x),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**n*ln(a*x),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int x^{n} \log \left (a x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^n*log(a*x),x, algorithm="giac")
[Out]