3.1035 \(\int \frac{1}{x \sqrt{a+(2+2 c-2 (1+c)) x^4}} \, dx\)

Optimal. Leaf size=8 \[ \frac{\log (x)}{\sqrt{a}} \]

[Out]

Log[x]/Sqrt[a]

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Rubi [A]  time = 0.00515621, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{\log (x)}{\sqrt{a}} \]

Antiderivative was successfully verified.

[In]  Int[1/(x*Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4]),x]

[Out]

Log[x]/Sqrt[a]

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Rubi in Sympy [A]  time = 1.48567, size = 7, normalized size = 0.88 \[ \frac{\log{\left (x \right )}}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x/a**(1/2),x)

[Out]

log(x)/sqrt(a)

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Mathematica [A]  time = 0.000910992, size = 8, normalized size = 1. \[ \frac{\log (x)}{\sqrt{a}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(x*Sqrt[a + (2 + 2*c - 2*(1 + c))*x^4]),x]

[Out]

Log[x]/Sqrt[a]

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Maple [A]  time = 0.002, size = 7, normalized size = 0.9 \[{\ln \left ( x \right ){\frac{1}{\sqrt{a}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x/a^(1/2),x)

[Out]

ln(x)/a^(1/2)

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Maxima [A]  time = 0.752277, size = 8, normalized size = 1. \[ \frac{\log \left (x\right )}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(a)*x),x, algorithm="maxima")

[Out]

log(x)/sqrt(a)

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Fricas [A]  time = 0.268515, size = 8, normalized size = 1. \[ \frac{\log \left (x\right )}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(a)*x),x, algorithm="fricas")

[Out]

log(x)/sqrt(a)

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Sympy [A]  time = 0.068428, size = 7, normalized size = 0.88 \[ \frac{\log{\left (x \right )}}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x/a**(1/2),x)

[Out]

log(x)/sqrt(a)

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GIAC/XCAS [A]  time = 0.262521, size = 9, normalized size = 1.12 \[ \frac{{\rm ln}\left ({\left | x \right |}\right )}{\sqrt{a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(sqrt(a)*x),x, algorithm="giac")

[Out]

ln(abs(x))/sqrt(a)