3.79.92 \(\int (-128+32 x-32 (i \pi +\log (-\frac {-2-\log (4)}{-1+\log (4)}))) \, dx\)

Optimal. Leaf size=27 \[ 16 \left (4+i \pi -x+\log \left (1-\frac {3}{1-\log (4)}\right )\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.15, number of steps used = 1, number of rules used = 0, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 16 x^2-32 x \left (4+i \pi +\log \left (-\frac {2+\log (4)}{1-\log (4)}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-128 + 32*x - 32*(I*Pi + Log[-((-2 - Log[4])/(-1 + Log[4]))]),x]

[Out]

16*x^2 - 32*x*(4 + I*Pi + Log[-((2 + Log[4])/(1 - Log[4]))])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=16 x^2-32 x \left (4+i \pi +\log \left (-\frac {2+\log (4)}{1-\log (4)}\right )\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 33, normalized size = 1.22 \begin {gather*} -128 x+16 x^2-32 x \left (i \pi +\log \left (-\frac {-2-\log (4)}{-1+\log (4)}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-128 + 32*x - 32*(I*Pi + Log[-((-2 - Log[4])/(-1 + Log[4]))]),x]

[Out]

-128*x + 16*x^2 - 32*x*(I*Pi + Log[-((-2 - Log[4])/(-1 + Log[4]))])

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fricas [A]  time = 1.09, size = 27, normalized size = 1.00 \begin {gather*} 16 \, x^{2} - 32 \, x \log \left (-\frac {2 \, {\left (\log \relax (2) + 1\right )}}{2 \, \log \relax (2) - 1}\right ) - 128 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log((-2*log(2)-2)/(2*log(2)-1))+32*x-128,x, algorithm="fricas")

[Out]

16*x^2 - 32*x*log(-2*(log(2) + 1)/(2*log(2) - 1)) - 128*x

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giac [A]  time = 0.15, size = 27, normalized size = 1.00 \begin {gather*} 16 \, x^{2} - 32 \, x \log \left (-\frac {2 \, {\left (\log \relax (2) + 1\right )}}{2 \, \log \relax (2) - 1}\right ) - 128 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log((-2*log(2)-2)/(2*log(2)-1))+32*x-128,x, algorithm="giac")

[Out]

16*x^2 - 32*x*log(-2*(log(2) + 1)/(2*log(2) - 1)) - 128*x

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maple [A]  time = 0.02, size = 27, normalized size = 1.00

method	result	size
gosper	\(-16 x \left (-x +2 \ln \left (\frac {-2 \ln \relax (2)-2}{2 \ln \relax (2)-1}\right )+8\right )\)	\(27\)
default	\(-32 \ln \left (\frac {-2 \ln \relax (2)-2}{2 \ln \relax (2)-1}\right ) x +16 x^{2}-128 x\)	\(29\)
norman	\(\left (-32 \ln \relax (2)-32 \ln \left (1+\ln \relax (2)\right )+32 \ln \left (2 \ln \relax (2)-1\right )-32 i \pi -128\right ) x +16 x^{2}\)	\(35\)
risch	\(-32 i \pi x -32 x \ln \relax (2)-32 \ln \left (1+\ln \relax (2)\right ) x +32 \ln \left (2 \ln \relax (2)-1\right ) x +16 x^{2}-128 x\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-32*ln((-2*ln(2)-2)/(2*ln(2)-1))+32*x-128,x,method=_RETURNVERBOSE)

[Out]

-16*x*(-x+2*ln((-2*ln(2)-2)/(2*ln(2)-1))+8)

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maxima [A]  time = 0.37, size = 27, normalized size = 1.00 \begin {gather*} 16 \, x^{2} - 32 \, x \log \left (-\frac {2 \, {\left (\log \relax (2) + 1\right )}}{2 \, \log \relax (2) - 1}\right ) - 128 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*log((-2*log(2)-2)/(2*log(2)-1))+32*x-128,x, algorithm="maxima")

[Out]

16*x^2 - 32*x*log(-2*(log(2) + 1)/(2*log(2) - 1)) - 128*x

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mupad [B]  time = 0.15, size = 26, normalized size = 0.96 \begin {gather*} 16\,x^2-x\,\left (32\,\ln \left (-\frac {\ln \relax (4)+2}{\ln \relax (4)-1}\right )+128\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(32*x - 32*log(-(2*log(2) + 2)/(2*log(2) - 1)) - 128,x)

[Out]

16*x^2 - x*(32*log(-(log(4) + 2)/(log(4) - 1)) + 128)

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sympy [A]  time = 0.07, size = 32, normalized size = 1.19 \begin {gather*} 16 x^{2} + x \left (-128 - 32 \log {\left (2 \log {\relax (2 )} + 2 \right )} + 32 \log {\left (-1 + 2 \log {\relax (2 )} \right )} - 32 i \pi \right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-32*ln((-2*ln(2)-2)/(2*ln(2)-1))+32*x-128,x)

[Out]

16*x**2 + x*(-128 - 32*log(2*log(2) + 2) + 32*log(-1 + 2*log(2)) - 32*I*pi)

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