3.52.35 \(\int (405+405 (i \pi +\log (4))) \, dx\) [5135]

Optimal. Leaf size=21 \[ 81 x \left (4+\frac {4+x}{x}\right ) (1+i \pi +\log (4)) \]

[Out]

81*(1+2*ln(2)+I*Pi)*((4+x)/x+4)*x

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Rubi [A]
time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.57, number of steps used = 1, number of rules used = 1, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {8} \begin {gather*} 405 x (1+i \pi +\log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[405 + 405*(I*Pi + Log[4]),x]

[Out]

405*x*(1 + I*Pi + Log[4])

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=405 x (1+i \pi +\log (4))\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 15, normalized size = 0.71 \begin {gather*} 405 x+405 x (i \pi +\log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[405 + 405*(I*Pi + Log[4]),x]

[Out]

405*x + 405*x*(I*Pi + Log[4])

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Maple [A]
time = 0.18, size = 13, normalized size = 0.62

method	result	size
default	\(x \left (810 \ln \left (2\right )+405 i \pi +405\right )\)	\(13\)
norman	\(x \left (810 \ln \left (2\right )+405 i \pi +405\right )\)	\(13\)
risch	\(810 x \ln \left (2\right )+405 i x \pi +405 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(810*ln(2)+405*I*Pi+405,x,method=_RETURNVERBOSE)

[Out]

x*(810*ln(2)+405*I*Pi+405)

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Maxima [A]
time = 0.27, size = 12, normalized size = 0.57 \begin {gather*} -405 \, {\left (-i \, \pi - 2 \, \log \left (2\right ) - 1\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(810*log(2)+405*I*pi+405,x, algorithm="maxima")

[Out]

-405*(-I*pi - 2*log(2) - 1)*x

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Fricas [A]
time = 0.36, size = 14, normalized size = 0.67 \begin {gather*} -405 \, {\left (-i \, \pi - 1\right )} x + 810 \, x \log \left (2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(810*log(2)+405*I*pi+405,x, algorithm="fricas")

[Out]

-405*(-I*pi - 1)*x + 810*x*log(2)

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Sympy [A]
time = 0.00, size = 12, normalized size = 0.57 \begin {gather*} x \left (405 + 810 \log {\left (2 \right )} + 405 i \pi \right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(810*ln(2)+405*I*pi+405,x)

[Out]

x*(405 + 810*log(2) + 405*I*pi)

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Giac [A]
time = 0.41, size = 12, normalized size = 0.57 \begin {gather*} -405 \, {\left (-i \, \pi - 2 \, \log \left (2\right ) - 1\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(810*log(2)+405*I*pi+405,x, algorithm="giac")

[Out]

-405*(-I*pi - 2*log(2) - 1)*x

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Mupad [B]
time = 0.00, size = 12, normalized size = 0.57 \begin {gather*} x\,\left (810\,\ln \left (2\right )+405+\Pi \,405{}\mathrm {i}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Pi*405i + 810*log(2) + 405,x)

[Out]

x*(Pi*405i + 810*log(2) + 405)

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