3.85.26 $\int (24x-12e^{4}x+(4x-2e^{4}x)\log (25)+e^e(-12+6e^4+(-2+e^4)\log (25)))dx$

Optimal. Leaf size=20 $$(2-e^4)x(-e^e+x)(6+\log (25))$$

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Rubi [B]  time = 0.02, antiderivative size = 43, normalized size of antiderivative = 2.15, number of steps used = 2, number of rules used = 1, integrand size = 42, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.024, Rules used = {6} $$\begin{array}{c}6(2-e^4)x^2+(2-e^4)x^2\log (25)-e^e(2-e^4)x(6+\log (25))\end{array}$$

Antiderivative was successfully verified.

[In]

Int[24*x - 12*E^4*x + (4*x - 2*E^4*x)*Log[25] + E^E*(-12 + 6*E^4 + (-2 + E^4)*Log[25]),x]

[Out]

6*(2 - E^4)*x^2 + (2 - E^4)*x^2*Log[25] - E^E*(2 - E^4)*x*(6 + Log[25])

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int ((24-12e^4)x+(4x-2e^{4}x)\log (25)+e^e(-12+6e^4+(-2+e^4)\log (25)))dx\\ & =6(2-e^4)x^2+(2-e^4)x^2\log (25)-e^e(2-e^4)x(6+\log (25))\end{array}\end{array}$$

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Mathematica [A]  time = 0.00, size = 21, normalized size = 1.05 $$\begin{array}{c}(-2+e^4)(e^{e}x-x^2)(6+\log (25))\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[24*x - 12*E^4*x + (4*x - 2*E^4*x)*Log[25] + E^E*(-12 + 6*E^4 + (-2 + E^4)*Log[25]),x]

[Out]

(-2 + E^4)*(E^E*x - x^2)*(6 + Log[25])

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fricas [B]  time = 0.77, size = 54, normalized size = 2.70 $$\begin{array}{c}-6x^2{e}^4+12x^2+2(3x{e}^4+(x{e}^4-2x)\log (5)-6x)e^e-2(x^2{e}^4-2x^2)\log (5)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(exp(4)-2)*log(5)+6*exp(4)-12)*exp(exp(1))+2*(-2*x*exp(4)+4*x)*log(5)-12*x*exp(4)+24*x,x, algorit
hm="fricas")

[Out]

-6*x^2*e^4 + 12*x^2 + 2*(3*x*e^4 + (x*e^4 - 2*x)*log(5) - 6*x)*e^e - 2*(x^2*e^4 - 2*x^2)*log(5)

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giac [B]  time = 0.13, size = 48, normalized size = 2.40 $$\begin{array}{c}-6x^2{e}^4+2((e^4-2)\log (5)+3e^4-6)x{e}^e+12x^2-2(x^2{e}^4-2x^2)\log (5)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(exp(4)-2)*log(5)+6*exp(4)-12)*exp(exp(1))+2*(-2*x*exp(4)+4*x)*log(5)-12*x*exp(4)+24*x,x, algorit
hm="giac")

[Out]

-6*x^2*e^4 + 2*((e^4 - 2)*log(5) + 3*e^4 - 6)*x*e^e + 12*x^2 - 2*(x^2*e^4 - 2*x^2)*log(5)

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maple [A]  time = 0.03, size = 26, normalized size = 1.30

method	result	size
gosper	$2({\mathrm{e}}^4\ln (5)-2\ln (5)+3{\mathrm{e}}^4-6)x({\mathrm{e}}^{\mathrm{e}}-x)$	$26$
default	$(2({\mathrm{e}}^4-2)\ln (5)+6{\mathrm{e}}^4-12){\mathrm{e}}^{\mathrm{e}}x+2\ln (5)(-x^2{\mathrm{e}}^4+2x^2)-6x^2{\mathrm{e}}^4+12x^2$	$50$
norman	$(-2{\mathrm{e}}^4\ln (5)+4\ln (5)-6{\mathrm{e}}^4+12)x^2+(2\ln (5){\mathrm{e}}^4{\mathrm{e}}^{\mathrm{e}}-4\ln (5){\mathrm{e}}^{\mathrm{e}}+6{\mathrm{e}}^4{\mathrm{e}}^{\mathrm{e}}-12{\mathrm{e}}^{\mathrm{e}})x$	$53$
risch	$2\ln (5){\mathrm{e}}^4{\mathrm{e}}^{\mathrm{e}}x-4\ln (5){\mathrm{e}}^{\mathrm{e}}x+6{\mathrm{e}}^4{\mathrm{e}}^{\mathrm{e}}x-12x{\mathrm{e}}^{\mathrm{e}}-2\ln (5)x^2{\mathrm{e}}^4+4x^2\ln (5)-6x^2{\mathrm{e}}^4+12x^2$	$62$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*(exp(4)-2)*ln(5)+6*exp(4)-12)*exp(exp(1))+2*(-2*x*exp(4)+4*x)*ln(5)-12*x*exp(4)+24*x,x,method=_RETURNVE
RBOSE)

[Out]

2*(exp(4)*ln(5)-2*ln(5)+3*exp(4)-6)*x*(exp(exp(1))-x)

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maxima [B]  time = 0.45, size = 48, normalized size = 2.40 $$\begin{array}{c}-6x^2{e}^4+2((e^4-2)\log (5)+3e^4-6)x{e}^e+12x^2-2(x^2{e}^4-2x^2)\log (5)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(exp(4)-2)*log(5)+6*exp(4)-12)*exp(exp(1))+2*(-2*x*exp(4)+4*x)*log(5)-12*x*exp(4)+24*x,x, algorit
hm="maxima")

[Out]

-6*x^2*e^4 + 2*((e^4 - 2)*log(5) + 3*e^4 - 6)*x*e^e + 12*x^2 - 2*(x^2*e^4 - 2*x^2)*log(5)

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mupad [B]  time = 0.12, size = 38, normalized size = 1.90 $$\begin{array}{c}2x({\mathrm{e}}^{\mathrm{e}+4}-2{\mathrm{e}}^{\mathrm{e}})(\ln (5)+3)-x^2(6{\mathrm{e}}^4+2\ln (5)({\mathrm{e}}^4-2)-12)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(24*x - 12*x*exp(4) + 2*log(5)*(4*x - 2*x*exp(4)) + exp(exp(1))*(6*exp(4) + 2*log(5)*(exp(4) - 2) - 12),x)

[Out]

2*x*(exp(exp(1) + 4) - 2*exp(exp(1)))*(log(5) + 3) - x^2*(6*exp(4) + 2*log(5)*(exp(4) - 2) - 12)

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sympy [B]  time = 0.07, size = 65, normalized size = 3.25 $$\begin{array}{c}{x}^2(-6e^4-2e^4\log (5)+4\log (5)+12)+x(-12e^e-4e^e\log (5)+2e^4{e}^e\log (5)+6e^4{e}^e)\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*(exp(4)-2)*ln(5)+6*exp(4)-12)*exp(exp(1))+2*(-2*x*exp(4)+4*x)*ln(5)-12*x*exp(4)+24*x,x)

[Out]

x**2*(-6*exp(4) - 2*exp(4)*log(5) + 4*log(5) + 12) + x*(-12*exp(E) - 4*exp(E)*log(5) + 2*exp(4)*exp(E)*log(5)
+ 6*exp(4)*exp(E))

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