3.87.48 \(\int 5 (i \pi +\log (4)) \, dx\)

Optimal. Leaf size=25 \[ 5 \left (-5+(i \pi +\log (4)) \left (x-\frac {\log ^2(5)}{\log ^2(3)}\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.44, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {8} \begin {gather*} 5 x (\log (4)+i \pi ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[5*(I*Pi + Log[4]),x]

[Out]

5*x*(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} &=5 x (i \pi +\log (4))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 0.48 \begin {gather*} 5 i \pi x+5 x \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[5*(I*Pi + Log[4]),x]

[Out]

(5*I)*Pi*x + 5*x*Log[4]

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fricas [A]  time = 0.42, size = 10, normalized size = 0.40 \begin {gather*} 5 i \, \pi x + 10 \, x \log \relax (2) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(2)+5*I*pi,x, algorithm="fricas")

[Out]

5*I*pi*x + 10*x*log(2)

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giac [A]  time = 0.16, size = 11, normalized size = 0.44 \begin {gather*} -5 \, {\left (-i \, \pi - 2 \, \log \relax (2)\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(2)+5*I*pi,x, algorithm="giac")

[Out]

-5*(-I*pi - 2*log(2))*x

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maple [A]  time = 0.01, size = 12, normalized size = 0.48

method	result	size
default	\(\left (10 \ln \relax (2)+5 i \pi \right ) x\)	\(12\)
norman	\(\left (10 \ln \relax (2)+5 i \pi \right ) x\)	\(12\)
risch	\(10 x \ln \relax (2)+5 i \pi x\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*ln(2)+5*I*Pi,x,method=_RETURNVERBOSE)

[Out]

(10*ln(2)+5*I*Pi)*x

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maxima [A]  time = 0.37, size = 11, normalized size = 0.44 \begin {gather*} -5 \, {\left (-i \, \pi - 2 \, \log \relax (2)\right )} x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*log(2)+5*I*pi,x, algorithm="maxima")

[Out]

-5*(-I*pi - 2*log(2))*x

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mupad [B]  time = 0.00, size = 11, normalized size = 0.44 \begin {gather*} x\,\left (10\,\ln \relax (2)+\Pi \,5{}\mathrm {i}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(Pi*5i + 10*log(2),x)

[Out]

x*(Pi*5i + 10*log(2))

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sympy [A]  time = 0.05, size = 10, normalized size = 0.40 \begin {gather*} x \left (10 \log {\relax (2 )} + 5 i \pi \right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*ln(2)+5*I*pi,x)

[Out]

x*(10*log(2) + 5*I*pi)

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