3.73.62 $\int \frac{-69177612+5618340x-172284x^2+2352x^3-12x^4+e^x(103766418+60706884x-5387844x^2+169344x^3-2334x^4+12x^5)}{23059204x^2-1872780x^3+57233x^4-780x^5+4x^6+e^x(-23059204x-44240826x^2+3697736x^3-114074x^4+1560x^5-8x^6)+e^{2x}(5764801+22588608x+21191226x^2-1824956x^3+56841x^4-780x^5+4x^6)}dx$

Optimal. Leaf size=33 $$\frac{3}{x-e^{x}x+\frac{1}{2}(-e^x+\frac{x^2}{(49-x{)}^2})}$$

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Rubi [F]  time = 4.56, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}\int \frac{-69177612+5618340x-172284x^2+2352x^3-12x^4+e^x(103766418+60706884x-5387844x^2+169344x^3-2334x^4+12x^5)}{23059204x^2-1872780x^3+57233x^4-780x^5+4x^6+e^x(-23059204x-44240826x^2+3697736x^3-114074x^4+1560x^5-8x^6)+e^{2x}(5764801+22588608x+21191226x^2-1824956x^3+56841x^4-780x^5+4x^6)}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(-69177612 + 5618340*x - 172284*x^2 + 2352*x^3 - 12*x^4 + E^x*(103766418 + 60706884*x - 5387844*x^2 + 1693
44*x^3 - 2334*x^4 + 12*x^5))/(23059204*x^2 - 1872780*x^3 + 57233*x^4 - 780*x^5 + 4*x^6 + E^x*(-23059204*x - 44
240826*x^2 + 3697736*x^3 - 114074*x^4 + 1560*x^5 - 8*x^6) + E^(2*x)*(5764801 + 22588608*x + 21191226*x^2 - 182
4956*x^3 + 56841*x^4 - 780*x^5 + 4*x^6)),x]

[Out]

2859738*Defer[Int][(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2))^(-2), x] + 69076476*Defer[Int][x/(E
^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2))^2, x] - 5631570*Defer[Int][x^2/(E^x*(-49 + x)^2*(1 + 2*x
) + x*(-4802 + 195*x - 2*x^2))^2, x] + 172284*Defer[Int][x^3/(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2
*x^2))^2, x] - 2346*Defer[Int][x^4/(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2))^2, x] + 12*Defer[In
t][x^5/(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2))^2, x] - 72037350*Defer[Int][1/((1 + 2*x)*(E^x*(
-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2))^2), x] + 13815*Defer[Int][(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4
802 + 195*x - 2*x^2))^(-1), x] - 582*Defer[Int][x/(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2)), x]
+ 6*Defer[Int][x^2/(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2)), x] + 29403*Defer[Int][1/((1 + 2*x)
*(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2))), x]

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{6(49-x)(-e^x(-49+x{)}^3(3+2x)+2(-117649+7154x-147x^2+x^3))}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx\\ & =6\int \frac{(49-x)(-e^x(-49+x{)}^3(3+2x)+2(-117649+7154x-147x^2+x^3))}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx\\ & =6\int (\frac{(-49+x{)}^2(3+2x)}{(1+2x)(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}+\frac{-11529602+12465992x+22086897x^2-1848476x^3+57037x^4-780x^5+4x^6}{(1+2x){(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2})dx\\ & =6\int \frac{(-49+x{)}^2(3+2x)}{(1+2x)(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}dx+6\int \frac{-11529602+12465992x+22086897x^2-1848476x^3+57037x^4-780x^5+4x^6}{(1+2x){(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx\\ & =6\int \frac{-11529602+12465992x+22086897x^2-1848476x^3+57037x^4-780x^5+4x^6}{(1+2x){(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx+6\int (\frac{4605}{2(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}-\frac{97x}{2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3}+\frac{x^2}{2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3}+\frac{9801}{2(1+2x)(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)})dx\\ & =6\int \frac{x^2}{2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3}dx+6\int (\frac{476623}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}+\frac{11512746x}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}-\frac{938595x^2}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}+\frac{28714x^3}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}-\frac{391x^4}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}+\frac{2x^5}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}-\frac{12006225}{(1+2x){(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2})dx-582\int \frac{x}{2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3}dx+13815\int \frac{1}{2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3}dx+29403\int \frac{1}{(1+2x)(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}dx\\ & =6\int \frac{x^2}{e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2)}dx+12\int \frac{x^5}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx-582\int \frac{x}{e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2)}dx-2346\int \frac{x^4}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx+13815\int \frac{1}{e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2)}dx+29403\int \frac{1}{(1+2x)(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}dx+172284\int \frac{x^3}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx+2859738\int \frac{1}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx-5631570\int \frac{x^2}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx+69076476\int \frac{x}{{(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx-72037350\int \frac{1}{(1+2x){(2401e^x-4802x+4704e^{x}x+195x^2-195e^x{x}^2-2x^3+2e^x{x}^3)}^2}dx\\ & =6\int \frac{x^2}{e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2)}dx+12\int \frac{x^5}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx-582\int \frac{x}{e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2)}dx-2346\int \frac{x^4}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx+13815\int \frac{1}{e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2)}dx+29403\int \frac{1}{(1+2x)(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}dx+172284\int \frac{x^3}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx+2859738\int \frac{1}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx-5631570\int \frac{x^2}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx+69076476\int \frac{x}{{(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx-72037350\int \frac{1}{(1+2x){(e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2))}^2}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.77, size = 36, normalized size = 1.09 $$\begin{array}{c}-\frac{6(-49+x{)}^2}{e^x(-49+x{)}^2(1+2x)+x(-4802+195x-2x^2)}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(-69177612 + 5618340*x - 172284*x^2 + 2352*x^3 - 12*x^4 + E^x*(103766418 + 60706884*x - 5387844*x^2
+ 169344*x^3 - 2334*x^4 + 12*x^5))/(23059204*x^2 - 1872780*x^3 + 57233*x^4 - 780*x^5 + 4*x^6 + E^x*(-23059204*
x - 44240826*x^2 + 3697736*x^3 - 114074*x^4 + 1560*x^5 - 8*x^6) + E^(2*x)*(5764801 + 22588608*x + 21191226*x^2
- 1824956*x^3 + 56841*x^4 - 780*x^5 + 4*x^6)),x]

[Out]

(-6*(-49 + x)^2)/(E^x*(-49 + x)^2*(1 + 2*x) + x*(-4802 + 195*x - 2*x^2))

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fricas [A]  time = 0.87, size = 45, normalized size = 1.36 $$\begin{array}{c}\frac{6(x^2-98x+2401)}{2x^3-195x^2-(2x^3-195x^2+4704x+2401)e^x+4802x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x^5-2334*x^4+169344*x^3-5387844*x^2+60706884*x+103766418)*exp(x)-12*x^4+2352*x^3-172284*x^2+561
8340*x-69177612)/((4*x^6-780*x^5+56841*x^4-1824956*x^3+21191226*x^2+22588608*x+5764801)*exp(x)^2+(-8*x^6+1560*
x^5-114074*x^4+3697736*x^3-44240826*x^2-23059204*x)*exp(x)+4*x^6-780*x^5+57233*x^4-1872780*x^3+23059204*x^2),x
, algorithm="fricas")

[Out]

6*(x^2 - 98*x + 2401)/(2*x^3 - 195*x^2 - (2*x^3 - 195*x^2 + 4704*x + 2401)*e^x + 4802*x)

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giac [A]  time = 0.30, size = 49, normalized size = 1.48 $$\begin{array}{c}-\frac{6(x^2-98x+2401)}{2x^3{e}^x-2x^3-195x^2{e}^x+195x^2+4704x{e}^x-4802x+2401e^x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x^5-2334*x^4+169344*x^3-5387844*x^2+60706884*x+103766418)*exp(x)-12*x^4+2352*x^3-172284*x^2+561
8340*x-69177612)/((4*x^6-780*x^5+56841*x^4-1824956*x^3+21191226*x^2+22588608*x+5764801)*exp(x)^2+(-8*x^6+1560*
x^5-114074*x^4+3697736*x^3-44240826*x^2-23059204*x)*exp(x)+4*x^6-780*x^5+57233*x^4-1872780*x^3+23059204*x^2),x
, algorithm="giac")

[Out]

-6*(x^2 - 98*x + 2401)/(2*x^3*e^x - 2*x^3 - 195*x^2*e^x + 195*x^2 + 4704*x*e^x - 4802*x + 2401*e^x)

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maple [A]  time = 0.10, size = 47, normalized size = 1.42

method	result	size
risch	$-\frac{6{(x-49)}^2}{2{\mathrm{e}}^x{x}^3-195{\mathrm{e}}^x{x}^2-2x^3+4704{\mathrm{e}}^{x}x+195x^2+2401{\mathrm{e}}^x-4802x}$	$47$
norman	$\frac{-6x^2+588x-14406}{2{\mathrm{e}}^x{x}^3-195{\mathrm{e}}^x{x}^2-2x^3+4704{\mathrm{e}}^{x}x+195x^2+2401{\mathrm{e}}^x-4802x}$	$51$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((12*x^5-2334*x^4+169344*x^3-5387844*x^2+60706884*x+103766418)*exp(x)-12*x^4+2352*x^3-172284*x^2+5618340*x
-69177612)/((4*x^6-780*x^5+56841*x^4-1824956*x^3+21191226*x^2+22588608*x+5764801)*exp(x)^2+(-8*x^6+1560*x^5-11
4074*x^4+3697736*x^3-44240826*x^2-23059204*x)*exp(x)+4*x^6-780*x^5+57233*x^4-1872780*x^3+23059204*x^2),x,metho
d=_RETURNVERBOSE)

[Out]

-6*(x-49)^2/(2*exp(x)*x^3-195*exp(x)*x^2-2*x^3+4704*exp(x)*x+195*x^2+2401*exp(x)-4802*x)

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maxima [A]  time = 0.45, size = 45, normalized size = 1.36 $$\begin{array}{c}\frac{6(x^2-98x+2401)}{2x^3-195x^2-(2x^3-195x^2+4704x+2401)e^x+4802x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x^5-2334*x^4+169344*x^3-5387844*x^2+60706884*x+103766418)*exp(x)-12*x^4+2352*x^3-172284*x^2+561
8340*x-69177612)/((4*x^6-780*x^5+56841*x^4-1824956*x^3+21191226*x^2+22588608*x+5764801)*exp(x)^2+(-8*x^6+1560*
x^5-114074*x^4+3697736*x^3-44240826*x^2-23059204*x)*exp(x)+4*x^6-780*x^5+57233*x^4-1872780*x^3+23059204*x^2),x
, algorithm="maxima")

[Out]

6*(x^2 - 98*x + 2401)/(2*x^3 - 195*x^2 - (2*x^3 - 195*x^2 + 4704*x + 2401)*e^x + 4802*x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 $$\begin{array}{c}\int \frac{5618340x+{\mathrm{e}}^x(12x^5-2334x^4+169344x^3-5387844x^2+60706884x+103766418)-172284x^2+2352x^3-12x^4-69177612}{23059204x^2-{\mathrm{e}}^x(8x^6-1560x^5+114074x^4-3697736x^3+44240826x^2+23059204x)-1872780x^3+57233x^4-780x^5+4x^6+{\mathrm{e}}^{2x}(4x^6-780x^5+56841x^4-1824956x^3+21191226x^2+22588608x+5764801)}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((5618340*x + exp(x)*(60706884*x - 5387844*x^2 + 169344*x^3 - 2334*x^4 + 12*x^5 + 103766418) - 172284*x^2 +
2352*x^3 - 12*x^4 - 69177612)/(23059204*x^2 - exp(x)*(23059204*x + 44240826*x^2 - 3697736*x^3 + 114074*x^4 -
1560*x^5 + 8*x^6) - 1872780*x^3 + 57233*x^4 - 780*x^5 + 4*x^6 + exp(2*x)*(22588608*x + 21191226*x^2 - 1824956*
x^3 + 56841*x^4 - 780*x^5 + 4*x^6 + 5764801)),x)

[Out]

int((5618340*x + exp(x)*(60706884*x - 5387844*x^2 + 169344*x^3 - 2334*x^4 + 12*x^5 + 103766418) - 172284*x^2 +
2352*x^3 - 12*x^4 - 69177612)/(23059204*x^2 - exp(x)*(23059204*x + 44240826*x^2 - 3697736*x^3 + 114074*x^4 -
1560*x^5 + 8*x^6) - 1872780*x^3 + 57233*x^4 - 780*x^5 + 4*x^6 + exp(2*x)*(22588608*x + 21191226*x^2 - 1824956*
x^3 + 56841*x^4 - 780*x^5 + 4*x^6 + 5764801)), x)

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sympy [A]  time = 0.59, size = 41, normalized size = 1.24 $$\begin{array}{c}\frac{-6x^2+588x-14406}{-2x^3+195x^2-4802x+(2x^3-195x^2+4704x+2401)e^x}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((12*x**5-2334*x**4+169344*x**3-5387844*x**2+60706884*x+103766418)*exp(x)-12*x**4+2352*x**3-172284*x
**2+5618340*x-69177612)/((4*x**6-780*x**5+56841*x**4-1824956*x**3+21191226*x**2+22588608*x+5764801)*exp(x)**2+
(-8*x**6+1560*x**5-114074*x**4+3697736*x**3-44240826*x**2-23059204*x)*exp(x)+4*x**6-780*x**5+57233*x**4-187278
0*x**3+23059204*x**2),x)

[Out]

(-6*x**2 + 588*x - 14406)/(-2*x**3 + 195*x**2 - 4802*x + (2*x**3 - 195*x**2 + 4704*x + 2401)*exp(x))

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