3.28.98 \(\int \frac {-1024 x^3+e^{2+2 e^{9 x}} (160 x^4-2880 e^{9 x} x^5)}{-4096+3840 e^{2+2 e^{9 x}} x-1200 e^{4+4 e^{9 x}} x^2+125 e^{6+6 e^{9 x}} x^3} \, dx\)

Optimal. Leaf size=23 \[ \frac {16 x^4}{\left (16-5 e^{2+2 e^{9 x}} x\right )^2} \]

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Rubi [F]  time = 2.35, 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 {gather*} \int \frac {-1024 x^3+e^{2+2 e^{9 x}} \left (160 x^4-2880 e^{9 x} x^5\right )}{-4096+3840 e^{2+2 e^{9 x}} x-1200 e^{4+4 e^{9 x}} x^2+125 e^{6+6 e^{9 x}} x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-1024*x^3 + E^(2 + 2*E^(9*x))*(160*x^4 - 2880*E^(9*x)*x^5))/(-4096 + 3840*E^(2 + 2*E^(9*x))*x - 1200*E^(4
+ 4*E^(9*x))*x^2 + 125*E^(6 + 6*E^(9*x))*x^3),x]

[Out]

-512*Defer[Int][x^3/(-16 + 5*E^(2 + 2*E^(9*x))*x)^3, x] - 2880*Defer[Int][(E^(2 + 2*E^(9*x) + 9*x)*x^5)/(-16 +
5*E^(2 + 2*E^(9*x))*x)^3, x] + 32*Defer[Int][x^3/(-16 + 5*E^(2 + 2*E^(9*x))*x)^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32 x^3 \left (32-5 e^{2+2 e^{9 x}} x+90 e^{2+2 e^{9 x}+9 x} x^2\right )}{\left (16-5 e^{2+2 e^{9 x}} x\right )^3} \, dx\\ &=32 \int \frac {x^3 \left (32-5 e^{2+2 e^{9 x}} x+90 e^{2+2 e^{9 x}+9 x} x^2\right )}{\left (16-5 e^{2+2 e^{9 x}} x\right )^3} \, dx\\ &=32 \int \left (-\frac {90 e^{2+2 e^{9 x}+9 x} x^5}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3}+\frac {x^3 \left (-32+5 e^{2+2 e^{9 x}} x\right )}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3}\right ) \, dx\\ &=32 \int \frac {x^3 \left (-32+5 e^{2+2 e^{9 x}} x\right )}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3} \, dx-2880 \int \frac {e^{2+2 e^{9 x}+9 x} x^5}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3} \, dx\\ &=32 \int \left (-\frac {16 x^3}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3}+\frac {x^3}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^2}\right ) \, dx-2880 \int \frac {e^{2+2 e^{9 x}+9 x} x^5}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3} \, dx\\ &=32 \int \frac {x^3}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^2} \, dx-512 \int \frac {x^3}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3} \, dx-2880 \int \frac {e^{2+2 e^{9 x}+9 x} x^5}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.47, size = 23, normalized size = 1.00 \begin {gather*} \frac {16 x^4}{\left (-16+5 e^{2+2 e^{9 x}} x\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1024*x^3 + E^(2 + 2*E^(9*x))*(160*x^4 - 2880*E^(9*x)*x^5))/(-4096 + 3840*E^(2 + 2*E^(9*x))*x - 120
0*E^(4 + 4*E^(9*x))*x^2 + 125*E^(6 + 6*E^(9*x))*x^3),x]

[Out]

(16*x^4)/(-16 + 5*E^(2 + 2*E^(9*x))*x)^2

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fricas [A]  time = 0.53, size = 35, normalized size = 1.52 \begin {gather*} \frac {16 \, x^{4}}{25 \, x^{2} e^{\left (4 \, e^{\left (9 \, x\right )} + 4\right )} - 160 \, x e^{\left (2 \, e^{\left (9 \, x\right )} + 2\right )} + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2880*x^5*exp(9*x)+160*x^4)*exp(2*exp(9*x)+2)-1024*x^3)/(125*x^3*exp(2*exp(9*x)+2)^3-1200*x^2*exp(
2*exp(9*x)+2)^2+3840*x*exp(2*exp(9*x)+2)-4096),x, algorithm="fricas")

[Out]

16*x^4/(25*x^2*e^(4*e^(9*x) + 4) - 160*x*e^(2*e^(9*x) + 2) + 256)

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giac [A]  time = 0.31, size = 35, normalized size = 1.52 \begin {gather*} \frac {16 \, x^{4}}{25 \, x^{2} e^{\left (4 \, e^{\left (9 \, x\right )} + 4\right )} - 160 \, x e^{\left (2 \, e^{\left (9 \, x\right )} + 2\right )} + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2880*x^5*exp(9*x)+160*x^4)*exp(2*exp(9*x)+2)-1024*x^3)/(125*x^3*exp(2*exp(9*x)+2)^3-1200*x^2*exp(
2*exp(9*x)+2)^2+3840*x*exp(2*exp(9*x)+2)-4096),x, algorithm="giac")

[Out]

16*x^4/(25*x^2*e^(4*e^(9*x) + 4) - 160*x*e^(2*e^(9*x) + 2) + 256)

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maple [A]  time = 0.05, size = 22, normalized size = 0.96

method	result	size
risch	\(\frac {16 x^{4}}{\left (5 x \,{\mathrm e}^{2 \,{\mathrm e}^{9 x}+2}-16\right )^{2}}\)	\(22\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2880*x^5*exp(9*x)+160*x^4)*exp(2*exp(9*x)+2)-1024*x^3)/(125*x^3*exp(2*exp(9*x)+2)^3-1200*x^2*exp(2*exp(
9*x)+2)^2+3840*x*exp(2*exp(9*x)+2)-4096),x,method=_RETURNVERBOSE)

[Out]

16*x^4/(5*x*exp(2*exp(9*x)+2)-16)^2

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maxima [A]  time = 0.41, size = 35, normalized size = 1.52 \begin {gather*} \frac {16 \, x^{4}}{25 \, x^{2} e^{\left (4 \, e^{\left (9 \, x\right )} + 4\right )} - 160 \, x e^{\left (2 \, e^{\left (9 \, x\right )} + 2\right )} + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2880*x^5*exp(9*x)+160*x^4)*exp(2*exp(9*x)+2)-1024*x^3)/(125*x^3*exp(2*exp(9*x)+2)^3-1200*x^2*exp(
2*exp(9*x)+2)^2+3840*x*exp(2*exp(9*x)+2)-4096),x, algorithm="maxima")

[Out]

16*x^4/(25*x^2*e^(4*e^(9*x) + 4) - 160*x*e^(2*e^(9*x) + 2) + 256)

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mupad [B]  time = 1.94, size = 35, normalized size = 1.52 \begin {gather*} \frac {16\,x^4}{25\,x^2\,{\mathrm {e}}^{4\,{\mathrm {e}}^{9\,x}}\,{\mathrm {e}}^4-160\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^{9\,x}}\,{\mathrm {e}}^2+256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(2*exp(9*x) + 2)*(2880*x^5*exp(9*x) - 160*x^4) + 1024*x^3)/(3840*x*exp(2*exp(9*x) + 2) - 1200*x^2*exp
(4*exp(9*x) + 4) + 125*x^3*exp(6*exp(9*x) + 6) - 4096),x)

[Out]

(16*x^4)/(25*x^2*exp(4*exp(9*x))*exp(4) - 160*x*exp(2*exp(9*x))*exp(2) + 256)

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sympy [A]  time = 0.19, size = 34, normalized size = 1.48 \begin {gather*} \frac {16 x^{4}}{25 x^{2} e^{4 e^{9 x} + 4} - 160 x e^{2 e^{9 x} + 2} + 256} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2880*x**5*exp(9*x)+160*x**4)*exp(2*exp(9*x)+2)-1024*x**3)/(125*x**3*exp(2*exp(9*x)+2)**3-1200*x**
2*exp(2*exp(9*x)+2)**2+3840*x*exp(2*exp(9*x)+2)-4096),x)

[Out]

16*x**4/(25*x**2*exp(4*exp(9*x) + 4) - 160*x*exp(2*exp(9*x) + 2) + 256)

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