3.85.71 $\int \frac{-10+6e^4\log (5)}{3e^4\log (5)}dx$

Optimal. Leaf size=17 $$4+2x-\frac{10x}{3e^4\log (5)}$$

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Rubi [A]  time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.94, number of steps used = 1, number of rules used = 1, integrand size = 20, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.050, Rules used = {8} $$\begin{array}{c}\frac{2}{3}x(3-\frac{5}{e^4\log (5)})\end{array}$$

Antiderivative was successfully verified.

[In]

Int[(-10 + 6*E^4*Log[5])/(3*E^4*Log[5]),x]

[Out]

(2*x*(3 - 5/(E^4*Log[5])))/3

Rule 8

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

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\frac{2}{3}x(3-\frac{5}{e^4\log (5)})\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 16, normalized size = 0.94 $$\begin{array}{c}2x-\frac{10x}{3e^4\log (5)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-10 + 6*E^4*Log[5])/(3*E^4*Log[5]),x]

[Out]

2*x - (10*x)/(3*E^4*Log[5])

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fricas [A]  time = 0.63, size = 19, normalized size = 1.12 $$\begin{array}{c}\frac{2(3x{e}^4\log (5)-5x)e^{(-4)}}{3\log (5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(6*exp(4)*log(5)-10)/exp(4)/log(5),x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.19, size = 17, normalized size = 1.00 $$\begin{array}{c}\frac{2(3e^4\log (5)-5)x{e}^{(-4)}}{3\log (5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(6*exp(4)*log(5)-10)/exp(4)/log(5),x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.02, size = 18, normalized size = 1.06

method	result	size
risch	$2{\mathrm{e}}^{-4}x{\mathrm{e}}^4-\frac{10{\mathrm{e}}^{-4}x}{3\ln (5)}$	$18$
default	$\frac{(6{\mathrm{e}}^4\ln (5)-10){\mathrm{e}}^{-4}x}{3\ln (5)}$	$20$
norman	$\frac{2(3{\mathrm{e}}^4\ln (5)-5){\mathrm{e}}^{-4}x}{3\ln (5)}$	$20$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*(6*exp(4)*ln(5)-10)/exp(4)/ln(5),x,method=_RETURNVERBOSE)

[Out]

2*exp(-4)*x*exp(4)-10/3*exp(-4)/ln(5)*x

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maxima [A]  time = 0.45, size = 17, normalized size = 1.00 $$\begin{array}{c}\frac{2(3e^4\log (5)-5)x{e}^{(-4)}}{3\log (5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(6*exp(4)*log(5)-10)/exp(4)/log(5),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 0.00, size = 16, normalized size = 0.94 $$\begin{array}{c}\frac{x{\mathrm{e}}^{-4}(2{\mathrm{e}}^4\ln (5)-\frac{10}{3})}{\ln (5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-4)*(2*exp(4)*log(5) - 10/3))/log(5),x)

[Out]

(x*exp(-4)*(2*exp(4)*log(5) - 10/3))/log(5)

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sympy [A]  time = 0.05, size = 19, normalized size = 1.12 $$\begin{array}{c}\frac{x(-\frac{10}{3}+2e^4\log (5))}{e^4\log (5)}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*(6*exp(4)*ln(5)-10)/exp(4)/ln(5),x)

[Out]

x*(-10/3 + 2*exp(4)*log(5))*exp(-4)/log(5)

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