3.72 \(\int \frac{\log (x)}{x^5} \, dx\)

Optimal. Leaf size=17 \[ -\frac{1}{16 x^4}-\frac{\log (x)}{4 x^4} \]

[Out]

-1/(16*x^4) - Log[x]/(4*x^4)

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Rubi [A]  time = 0.0174426, antiderivative size = 17, 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 \[ -\frac{1}{16 x^4}-\frac{\log (x)}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Int[Log[x]/x^5,x]

[Out]

-1/(16*x^4) - Log[x]/(4*x^4)

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Rubi in Sympy [A]  time = 1.14663, size = 15, normalized size = 0.88 \[ - \frac{\log{\left (x \right )}}{4 x^{4}} - \frac{1}{16 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(ln(x)/x**5,x)

[Out]

-log(x)/(4*x**4) - 1/(16*x**4)

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Mathematica [A]  time = 0.00210101, size = 17, normalized size = 1. \[ -\frac{1}{16 x^4}-\frac{\log (x)}{4 x^4} \]

Antiderivative was successfully verified.

[In]  Integrate[Log[x]/x^5,x]

[Out]

-1/(16*x^4) - Log[x]/(4*x^4)

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Maple [A]  time = 0.001, size = 14, normalized size = 0.8 \[ -{\frac{1}{16\,{x}^{4}}}-{\frac{\ln \left ( x \right ) }{4\,{x}^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(ln(x)/x^5,x)

[Out]

-1/16/x^4-1/4*ln(x)/x^4

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Maxima [A]  time = 1.35203, size = 18, normalized size = 1.06 \[ -\frac{\log \left (x\right )}{4 \, x^{4}} - \frac{1}{16 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(log(x)/x^5,x, algorithm="maxima")

[Out]

-1/4*log(x)/x^4 - 1/16/x^4

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Fricas [A]  time = 0.219842, size = 15, normalized size = 0.88 \[ -\frac{4 \, \log \left (x\right ) + 1}{16 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(log(x)/x^5,x, algorithm="fricas")

[Out]

-1/16*(4*log(x) + 1)/x^4

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Sympy [A]  time = 0.088194, size = 15, normalized size = 0.88 \[ - \frac{\log{\left (x \right )}}{4 x^{4}} - \frac{1}{16 x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(ln(x)/x**5,x)

[Out]

-log(x)/(4*x**4) - 1/(16*x**4)

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GIAC/XCAS [A]  time = 0.232927, size = 18, normalized size = 1.06 \[ -\frac{{\rm ln}\left (x\right )}{4 \, x^{4}} - \frac{1}{16 \, x^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(log(x)/x^5,x, algorithm="giac")

[Out]

-1/4*ln(x)/x^4 - 1/16/x^4