Optimal. Leaf size=26 \[ \frac{x^{m+1} \log (x)}{m+1}-\frac{x^{m+1}}{(m+1)^2} \]
[Out]
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Rubi [A] time = 0.0210334, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{x^{m+1} \log (x)}{m+1}-\frac{x^{m+1}}{(m+1)^2} \]
Antiderivative was successfully verified.
[In] Int[x^m*Log[x],x]
[Out]
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Rubi in Sympy [A] time = 1.60283, size = 20, normalized size = 0.77 \[ \frac{x^{m + 1} \log{\left (x \right )}}{m + 1} - \frac{x^{m + 1}}{\left (m + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**m*ln(x),x)
[Out]
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Mathematica [A] time = 0.0138108, size = 19, normalized size = 0.73 \[ \frac{x^{m+1} ((m+1) \log (x)-1)}{(m+1)^2} \]
Antiderivative was successfully verified.
[In] Integrate[x^m*Log[x],x]
[Out]
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Maple [A] time = 0.013, size = 34, normalized size = 1.3 \[{\frac{x\ln \left ( x \right ){{\rm e}^{m\ln \left ( x \right ) }}}{1+m}}-{\frac{x{{\rm e}^{m\ln \left ( x \right ) }}}{{m}^{2}+2\,m+1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^m*ln(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^m*log(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214468, size = 34, normalized size = 1.31 \[ \frac{{\left ({\left (m + 1\right )} x \log \left (x\right ) - x\right )} x^{m}}{m^{2} + 2 \, m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m*log(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**m*ln(x),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int x^{m} \log \left (x\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^m*log(x),x, algorithm="giac")
[Out]