3.85.13 $\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}(11520+624x-96x^2)}{225x^{17}-30x^{18}+x^{19}}dx$

Optimal. Leaf size=21 $$e^{\frac{16e^{-2x}}{(-5+\frac{x}{3})x^{16}}}$$

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Rubi [F]  time = 3.54, 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 = {} $$\begin{array}{c}\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}(11520+624x-96x^2)}{225x^{17}-30x^{18}+x^{19}}dx\end{array}$$

Verification is not applicable to the result.

[In]

Int[(E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))*(11520 + 624*x - 96*x^2))/(225*x^17 - 30*x^18 + x^19),x]

[Out]

(-16*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/(-15 + x)^2, x])/2189469451904296875 - (32*Defer[Int
][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/(-15 + x), x])/2189469451904296875 + (256*Defer[Int][E^(-2*x + 48/
(E^(2*x)*(-15*x^16 + x^17)))/x^17, x])/5 + (48*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^16, x])/
5 + (704*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^15, x])/1125 + (688*Defer[Int][E^(-2*x + 48/(E
^(2*x)*(-15*x^16 + x^17)))/x^14, x])/16875 + (224*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^13, x
])/84375 + (656*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^12, x])/3796875 + (128*Defer[Int][E^(-2
*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^11, x])/11390625 + (208*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^
17)))/x^10, x])/284765625 + (608*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^9, x])/12814453125 + (
592*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^8, x])/192216796875 + (64*Defer[Int][E^(-2*x + 48/(
E^(2*x)*(-15*x^16 + x^17)))/x^7, x])/320361328125 + (112*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/
x^6, x])/8649755859375 + (544*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^5, x])/648731689453125 +
(176*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x^4, x])/3243658447265625 + (512*Defer[Int][E^(-2*x
+ 48/(E^(2*x)*(-15*x^16 + x^17)))/x^3, x])/145964630126953125 + (496*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^1
6 + x^17)))/x^2, x])/2189469451904296875 + (32*Defer[Int][E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))/x, x])/218
9469451904296875

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}(11520+624x-96x^2)}{x^{17}(225-30x+x^2)}dx\\ & =\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}(11520+624x-96x^2)}{(-15+x{)}^2{x}^{17}}dx\\ & =\int (-\frac{16e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{2189469451904296875(-15+x{)}^2}-\frac{32e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{2189469451904296875(-15+x)}+\frac{256e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{5x^{17}}+\frac{48e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{5x^{16}}+\frac{704e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{1125x^{15}}+\frac{688e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{16875x^{14}}+\frac{224e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{84375x^{13}}+\frac{656e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{3796875x^{12}}+\frac{128e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{11390625x^{11}}+\frac{208e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{284765625x^{10}}+\frac{608e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{12814453125x^9}+\frac{592e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{192216796875x^8}+\frac{64e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{320361328125x^7}+\frac{112e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{8649755859375x^6}+\frac{544e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{648731689453125x^5}+\frac{176e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{3243658447265625x^4}+\frac{512e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{145964630126953125x^3}+\frac{496e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{2189469451904296875x^2}+\frac{32e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{2189469451904296875x})dx\\ & =-\frac{16\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{(-15+x{)}^2}dx}{2189469451904296875}-\frac{32\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{-15+x}dx}{2189469451904296875}+\frac{32\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x}dx}{2189469451904296875}+\frac{496\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^2}dx}{2189469451904296875}+\frac{512\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^3}dx}{145964630126953125}+\frac{176\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^4}dx}{3243658447265625}+\frac{544\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^5}dx}{648731689453125}+\frac{112\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^6}dx}{8649755859375}+\frac{64\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^7}dx}{320361328125}+\frac{592\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^8}dx}{192216796875}+\frac{608\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^9}dx}{12814453125}+\frac{208\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{10}}dx}{284765625}+\frac{128\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{11}}dx}{11390625}+\frac{656\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{12}}dx}{3796875}+\frac{224\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{13}}dx}{84375}+\frac{688\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{14}}dx}{16875}+\frac{704\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{15}}dx}{1125}+\frac{48}{5}\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{16}}dx+\frac{256}{5}\int \frac{e^{-2x+\frac{48e^{-2x}}{-15x^{16}+x^{17}}}}{x^{17}}dx\end{array}\end{array}$$

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Mathematica [A]  time = 0.63, size = 17, normalized size = 0.81 $$\begin{array}{c}{e}^{\frac{48e^{-2x}}{(-15+x)x^{16}}}\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[(E^(-2*x + 48/(E^(2*x)*(-15*x^16 + x^17)))*(11520 + 624*x - 96*x^2))/(225*x^17 - 30*x^18 + x^19),x]

[Out]

E^(48/(E^(2*x)*(-15 + x)*x^16))

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fricas [B]  time = 1.03, size = 33, normalized size = 1.57 $$\begin{array}{c}{e}^{(2x-\frac{2(x^{18}-15x^{17}-24e^{(-2x)})}{x^{17}-15x^{16}})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-96*x^2+624*x+11520)*exp(48/(x^17-15*x^16)/exp(x)^2)/(x^19-30*x^18+225*x^17)/exp(x)^2,x, algorithm=
"fricas")

[Out]

e^(2*x - 2*(x^18 - 15*x^17 - 24*e^(-2*x))/(x^17 - 15*x^16))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 $$\begin{array}{c}\int -\frac{48(2x^2-13x-240)e^{(-2x+\frac{48e^{(-2x)}}{x^{17}-15x^{16}})}}{x^{19}-30x^{18}+225x^{17}}dx\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-96*x^2+624*x+11520)*exp(48/(x^17-15*x^16)/exp(x)^2)/(x^19-30*x^18+225*x^17)/exp(x)^2,x, algorithm=
"giac")

[Out]

integrate(-48*(2*x^2 - 13*x - 240)*e^(-2*x + 48*e^(-2*x)/(x^17 - 15*x^16))/(x^19 - 30*x^18 + 225*x^17), x)

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maple [A]  time = 0.05, size = 16, normalized size = 0.76

method	result	size
risch	${\mathrm{e}}^{\frac{48{\mathrm{e}}^{-2x}}{x^{16}(x-15)}}$	$16$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-96*x^2+624*x+11520)*exp(48/(x^17-15*x^16)/exp(x)^2)/(x^19-30*x^18+225*x^17)/exp(x)^2,x,method=_RETURNVER
BOSE)

[Out]

exp(48*exp(-2*x)/x^16/(x-15))

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maxima [B]  time = 0.69, size = 157, normalized size = 7.48 $$\begin{array}{c}{e}^{(\frac{16e^{(-2x)}}{2189469451904296875(x-15)}-\frac{16e^{(-2x)}}{2189469451904296875x}-\frac{16e^{(-2x)}}{145964630126953125x^2}-\frac{16e^{(-2x)}}{9730975341796875x^3}-\frac{16e^{(-2x)}}{648731689453125x^4}-\frac{16e^{(-2x)}}{43248779296875x^5}-\frac{16e^{(-2x)}}{2883251953125x^6}-\frac{16e^{(-2x)}}{192216796875x^7}-\frac{16e^{(-2x)}}{12814453125x^8}-\frac{16e^{(-2x)}}{854296875x^9}-\frac{16e^{(-2x)}}{56953125x^{10}}-\frac{16e^{(-2x)}}{3796875x^{11}}-\frac{16e^{(-2x)}}{253125x^{12}}-\frac{16e^{(-2x)}}{16875x^{13}}-\frac{16e^{(-2x)}}{1125x^{14}}-\frac{16e^{(-2x)}}{75x^{15}}-\frac{16e^{(-2x)}}{5x^{16}})}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-96*x^2+624*x+11520)*exp(48/(x^17-15*x^16)/exp(x)^2)/(x^19-30*x^18+225*x^17)/exp(x)^2,x, algorithm=
"maxima")

[Out]

e^(16/2189469451904296875*e^(-2*x)/(x - 15) - 16/2189469451904296875*e^(-2*x)/x - 16/145964630126953125*e^(-2*
x)/x^2 - 16/9730975341796875*e^(-2*x)/x^3 - 16/648731689453125*e^(-2*x)/x^4 - 16/43248779296875*e^(-2*x)/x^5 -
16/2883251953125*e^(-2*x)/x^6 - 16/192216796875*e^(-2*x)/x^7 - 16/12814453125*e^(-2*x)/x^8 - 16/854296875*e^(
-2*x)/x^9 - 16/56953125*e^(-2*x)/x^10 - 16/3796875*e^(-2*x)/x^11 - 16/253125*e^(-2*x)/x^12 - 16/16875*e^(-2*x)
/x^13 - 16/1125*e^(-2*x)/x^14 - 16/75*e^(-2*x)/x^15 - 16/5*e^(-2*x)/x^16)

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mupad [B]  time = 5.45, size = 20, normalized size = 0.95 $$\begin{array}{c}{\mathrm{e}}^{-\frac{48{\mathrm{e}}^{-2x}}{15x^{16}-x^{17}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(48*exp(-2*x))/(15*x^16 - x^17))*exp(-2*x)*(624*x - 96*x^2 + 11520))/(225*x^17 - 30*x^18 + x^19),x)

[Out]

exp(-(48*exp(-2*x))/(15*x^16 - x^17))

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sympy [A]  time = 0.28, size = 15, normalized size = 0.71 $$\begin{array}{c}{e}^{\frac{48e^{-2x}}{x^{17}-15x^{16}}}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-96*x**2+624*x+11520)*exp(48/(x**17-15*x**16)/exp(x)**2)/(x**19-30*x**18+225*x**17)/exp(x)**2,x)

[Out]

exp(48*exp(-2*x)/(x**17 - 15*x**16))

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