3.17.73 $\int \frac{-9+5\log (\frac{1}{4}(6+e^4-\log (2)))}{\log (\frac{1}{4}(6+e^4-\log (2)))}dx$

Optimal. Leaf size=22 $$x(5-\frac{9}{\log \left(\frac{1}{4}(6+e^4-\log (2))\right)})$$

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Rubi [A]  time = 0.01, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 35, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.029, Rules used = {8} $$\begin{array}{c}x(5-\frac{9}{\log \left(\frac{1}{4}(6+e^4-\log (2))\right)})\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(-9 + 5*Log[(6 + E^4 - Log[2])/4])/Log[(6 + E^4 - Log[2])/4],x]

[Out]

x*(5 - 9/Log[(6 + E^4 - Log[2])/4])

Rule 8

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

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =x(5-\frac{9}{\log \left(\frac{1}{4}(6+e^4-\log (2))\right)})\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 23, normalized size = 1.05 $$\begin{array}{c}5x-\frac{9x}{\log \left(\frac{1}{4}(6+e^4-\log (2))\right)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-9 + 5*Log[(6 + E^4 - Log[2])/4])/Log[(6 + E^4 - Log[2])/4],x]

[Out]

5*x - (9*x)/Log[(6 + E^4 - Log[2])/4]

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fricas [A]  time = 0.71, size = 32, normalized size = 1.45 $$\begin{array}{c}\frac{5x\log (\frac{1}{4}{e}^4-\frac{1}{4}\log (2)+\frac{3}{2})-9x}{\log (\frac{1}{4}{e}^4-\frac{1}{4}\log (2)+\frac{3}{2})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*log(-1/4*log(2)+1/4*exp(4)+3/2)-9)/log(-1/4*log(2)+1/4*exp(4)+3/2),x, algorithm="fricas")

[Out]

(5*x*log(1/4*e^4 - 1/4*log(2) + 3/2) - 9*x)/log(1/4*e^4 - 1/4*log(2) + 3/2)

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giac [A]  time = 0.16, size = 30, normalized size = 1.36 $$\begin{array}{c}\frac{x(5\log (\frac{1}{4}{e}^4-\frac{1}{4}\log (2)+\frac{3}{2})-9)}{\log (\frac{1}{4}{e}^4-\frac{1}{4}\log (2)+\frac{3}{2})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*log(-1/4*log(2)+1/4*exp(4)+3/2)-9)/log(-1/4*log(2)+1/4*exp(4)+3/2),x, algorithm="giac")

[Out]

x*(5*log(1/4*e^4 - 1/4*log(2) + 3/2) - 9)/log(1/4*e^4 - 1/4*log(2) + 3/2)

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maple [A]  time = 0.03, size = 31, normalized size = 1.41

method	result	size
default	$\frac{(5\ln (-\frac{\ln (2)}{4}+\frac{{\mathrm{e}}^4}{4}+\frac{3}{2})-9)x}{\ln (-\frac{\ln (2)}{4}+\frac{{\mathrm{e}}^4}{4}+\frac{3}{2})}$	$31$
norman	$\frac{(10\ln (2)-5\ln (-\ln (2)+{\mathrm{e}}^4+6)+9)x}{2\ln (2)-\ln (-\ln (2)+{\mathrm{e}}^4+6)}$	$38$
risch	$-\frac{10x\ln (2)}{-2\ln (2)+\ln (-\ln (2)+{\mathrm{e}}^4+6)}+\frac{5x\ln (-\ln (2)+{\mathrm{e}}^4+6)}{-2\ln (2)+\ln (-\ln (2)+{\mathrm{e}}^4+6)}-\frac{9x}{-2\ln (2)+\ln (-\ln (2)+{\mathrm{e}}^4+6)}$	$70$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*ln(-1/4*ln(2)+1/4*exp(4)+3/2)-9)/ln(-1/4*ln(2)+1/4*exp(4)+3/2),x,method=_RETURNVERBOSE)

[Out]

(5*ln(-1/4*ln(2)+1/4*exp(4)+3/2)-9)/ln(-1/4*ln(2)+1/4*exp(4)+3/2)*x

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maxima [A]  time = 0.51, size = 30, normalized size = 1.36 $$\begin{array}{c}\frac{x(5\log (\frac{1}{4}{e}^4-\frac{1}{4}\log (2)+\frac{3}{2})-9)}{\log (\frac{1}{4}{e}^4-\frac{1}{4}\log (2)+\frac{3}{2})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*log(-1/4*log(2)+1/4*exp(4)+3/2)-9)/log(-1/4*log(2)+1/4*exp(4)+3/2),x, algorithm="maxima")

[Out]

x*(5*log(1/4*e^4 - 1/4*log(2) + 3/2) - 9)/log(1/4*e^4 - 1/4*log(2) + 3/2)

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mupad [B]  time = 0.00, size = 30, normalized size = 1.36 $$\begin{array}{c}\frac{x(5\ln (\frac{{\mathrm{e}}^4}{4}-\frac{\ln (2)}{4}+\frac{3}{2})-9)}{\ln (\frac{{\mathrm{e}}^4}{4}-\frac{\ln (2)}{4}+\frac{3}{2})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5*log(exp(4)/4 - log(2)/4 + 3/2) - 9)/log(exp(4)/4 - log(2)/4 + 3/2),x)

[Out]

(x*(5*log(exp(4)/4 - log(2)/4 + 3/2) - 9))/log(exp(4)/4 - log(2)/4 + 3/2)

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sympy [A]  time = 0.06, size = 34, normalized size = 1.55 $$\begin{array}{c}\frac{x(-9+5\log (-\frac{\log (2)}{4}+\frac{3}{2}+\frac{e^4}{4}))}{\log (-\frac{\log (2)}{4}+\frac{3}{2}+\frac{e^4}{4})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((5*ln(-1/4*ln(2)+1/4*exp(4)+3/2)-9)/ln(-1/4*ln(2)+1/4*exp(4)+3/2),x)

[Out]

x*(-9 + 5*log(-log(2)/4 + 3/2 + exp(4)/4))/log(-log(2)/4 + 3/2 + exp(4)/4)

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