Optimal. Leaf size=43 \[ -\frac{4}{3} \text{Ei}(-2 \log (x))-\frac{1}{3 x^2 \log ^3(x)}+\frac{1}{3 x^2 \log ^2(x)}-\frac{2}{3 x^2 \log (x)} \]
[Out]
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Rubi [A] time = 0.0905949, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375 \[ -\frac{4}{3} \text{Ei}(-2 \log (x))-\frac{1}{3 x^2 \log ^3(x)}+\frac{1}{3 x^2 \log ^2(x)}-\frac{2}{3 x^2 \log (x)} \]
Antiderivative was successfully verified.
[In] Int[1/(x^3*Log[x]^4),x]
[Out]
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Rubi in Sympy [A] time = 4.31623, size = 44, normalized size = 1.02 \[ - \frac{4 \operatorname{Ei}{\left (- 2 \log{\left (x \right )} \right )}}{3} - \frac{2}{3 x^{2} \log{\left (x \right )}} + \frac{1}{3 x^{2} \log{\left (x \right )}^{2}} - \frac{1}{3 x^{2} \log{\left (x \right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**3/ln(x)**4,x)
[Out]
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Mathematica [A] time = 0.00837652, size = 43, normalized size = 1. \[ -\frac{4}{3} \text{Ei}(-2 \log (x))-\frac{1}{3 x^2 \log ^3(x)}+\frac{1}{3 x^2 \log ^2(x)}-\frac{2}{3 x^2 \log (x)} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x^3*Log[x]^4),x]
[Out]
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Maple [A] time = 0.01, size = 37, normalized size = 0.9 \[ -{\frac{1}{3\,{x}^{2} \left ( \ln \left ( x \right ) \right ) ^{3}}}+{\frac{1}{3\,{x}^{2} \left ( \ln \left ( x \right ) \right ) ^{2}}}-{\frac{2}{3\,{x}^{2}\ln \left ( x \right ) }}+{\frac{4\,{\it Ei} \left ( 1,2\,\ln \left ( x \right ) \right ) }{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^3/ln(x)^4,x)
[Out]
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Maxima [A] time = 1.79426, size = 11, normalized size = 0.26 \[ -8 \, \Gamma \left (-3, 2 \, \log \left (x\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^3*log(x)^4),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[ -\frac{4 \, x^{2} \log \left (x\right )^{3} log_integral\left (\frac{1}{x^{2}}\right ) + 2 \, \log \left (x\right )^{2} - \log \left (x\right ) + 1}{3 \, x^{2} \log \left (x\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^3*log(x)^4),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{4 \int \frac{1}{x^{3} \log{\left (x \right )}}\, dx}{3} + \frac{- 2 \log{\left (x \right )}^{2} + \log{\left (x \right )} - 1}{3 x^{2} \log{\left (x \right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**3/ln(x)**4,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x^{3} \log \left (x\right )^{4}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(x^3*log(x)^4),x, algorithm="giac")
[Out]