3.93.16 \(\int \frac {90}{e \log (2)} \, dx\)

Optimal. Leaf size=12 \[ 2+\frac {90 x}{e \log (2)} \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.83, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \begin {gather*} \frac {90 x}{e \log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[90/(E*Log[2]),x]

[Out]

(90*x)/(E*Log[2])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {90 x}{e \log (2)}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} \frac {90 x}{e \log (2)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[90/(E*Log[2]),x]

[Out]

(90*x)/(E*Log[2])

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fricas [A]  time = 0.72, size = 9, normalized size = 0.75 \begin {gather*} \frac {90 \, x e^{\left (-1\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90/exp(1)/log(2),x, algorithm="fricas")

[Out]

90*x*e^(-1)/log(2)

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giac [A]  time = 0.15, size = 9, normalized size = 0.75 \begin {gather*} \frac {90 \, x e^{\left (-1\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90/exp(1)/log(2),x, algorithm="giac")

[Out]

90*x*e^(-1)/log(2)

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maple [A]  time = 0.02, size = 10, normalized size = 0.83

method	result	size
risch	\(\frac {90 \,{\mathrm e}^{-1} x}{\ln \relax (2)}\)	\(10\)
default	\(\frac {90 \,{\mathrm e}^{-1} x}{\ln \relax (2)}\)	\(12\)
norman	\(\frac {90 \,{\mathrm e}^{-1} x}{\ln \relax (2)}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(90/exp(1)/ln(2),x,method=_RETURNVERBOSE)

[Out]

90/ln(2)*exp(-1)*x

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maxima [A]  time = 0.36, size = 9, normalized size = 0.75 \begin {gather*} \frac {90 \, x e^{\left (-1\right )}}{\log \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90/exp(1)/log(2),x, algorithm="maxima")

[Out]

90*x*e^(-1)/log(2)

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mupad [B]  time = 0.00, size = 9, normalized size = 0.75 \begin {gather*} \frac {90\,x\,{\mathrm {e}}^{-1}}{\ln \relax (2)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((90*exp(-1))/log(2),x)

[Out]

(90*x*exp(-1))/log(2)

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sympy [A]  time = 0.02, size = 8, normalized size = 0.67 \begin {gather*} \frac {90 x}{e \log {\relax (2 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(90/exp(1)/ln(2),x)

[Out]

90*x*exp(-1)/log(2)

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