3.105 \(\int \frac {\log (-1+4 x+4 \sqrt {(-1+x) x})}{x} \, dx\)

Optimal. Leaf size=26 \[ \text {Int}\left (\frac {\log \left (4 \sqrt {x^2-x}+4 x-1\right )}{x},x\right ) \]

[Out]

CannotIntegrate(ln(-1+4*x+4*(x^2-x)^(1/2))/x,x)

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Rubi [A]  time = 0.08, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\log \left (-1+4 x+4 \sqrt {(-1+x) x}\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x,x]

[Out]

Defer[Int][Log[-1 + 4*x + 4*Sqrt[-x + x^2]]/x, x]

Rubi steps

\begin {align*} \int \frac {\log \left (-1+4 x+4 \sqrt {(-1+x) x}\right )}{x} \, dx &=\int \frac {\log \left (-1+4 x+4 \sqrt {-x+x^2}\right )}{x} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.48, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (-1+4 x+4 \sqrt {(-1+x) x}\right )}{x} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x,x]

[Out]

Integrate[Log[-1 + 4*x + 4*Sqrt[(-1 + x)*x]]/x, x]

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fricas [A]  time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\log \left (4 \, x + 4 \, \sqrt {x^{2} - x} - 1\right )}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(-1+4*x+4*((-1+x)*x)^(1/2))/x,x, algorithm="fricas")

[Out]

integral(log(4*x + 4*sqrt(x^2 - x) - 1)/x, x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (4 \, x + 4 \, \sqrt {{\left (x - 1\right )} x} - 1\right )}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(-1+4*x+4*((-1+x)*x)^(1/2))/x,x, algorithm="giac")

[Out]

integrate(log(4*x + 4*sqrt((x - 1)*x) - 1)/x, x)

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maple [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {\ln \left (4 x -1+4 \sqrt {\left (x -1\right ) x}\right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(4*x-1+4*((x-1)*x)^(1/2))/x,x)

[Out]

int(ln(4*x-1+4*((x-1)*x)^(1/2))/x,x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log \left (4 \, x + 4 \, \sqrt {{\left (x - 1\right )} x} - 1\right )}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(-1+4*x+4*((-1+x)*x)^(1/2))/x,x, algorithm="maxima")

[Out]

integrate(log(4*x + 4*sqrt((x - 1)*x) - 1)/x, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {\ln \left (4\,x+4\,\sqrt {x\,\left (x-1\right )}-1\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(4*x + 4*(x*(x - 1))^(1/2) - 1)/x,x)

[Out]

int(log(4*x + 4*(x*(x - 1))^(1/2) - 1)/x, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log {\left (4 x + 4 \sqrt {x^{2} - x} - 1 \right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(-1+4*x+4*((-1+x)*x)**(1/2))/x,x)

[Out]

Integral(log(4*x + 4*sqrt(x**2 - x) - 1)/x, x)

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