\(\int \frac {20 x^5+e^{15} (-800-640 x^2+2 x^5-20 x^6)+e^{30} (500 x+480 x^3+64 x^5+5 x^7)}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx\) [1241]

Optimal result

Integrand size = 74, antiderivative size = 29 \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=5 x+\frac {4 \left (4+\frac {5}{x^2}\right )^2+x}{\frac {2}{e^{15}}-x} \]

[Out]

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

Rubi [F(-1)]

Timed out. \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=\text {\$Aborted} \]

[In]

Int[(20*x^5 + E^15*(-800 - 640*x^2 + 2*x^5 - 20*x^6) + E^30*(500*x + 480*x^3 + 64*x^5 + 5*x^7))/(4*x^5 - 4*E^1
5*x^6 + E^30*x^7),x]

[Out]

$Aborted

Rubi steps \begin{align*} \text {integral}& = \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{x^5 \left (4-4 e^{15} x+e^{30} x^2\right )} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.03 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.55 \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=\frac {-2 x^4 (1+5 x)+e^{15} \left (-100-160 x^2-64 x^4+5 x^6\right )}{x^4 \left (-2+e^{15} x\right )} \]

[In]

Integrate[(20*x^5 + E^15*(-800 - 640*x^2 + 2*x^5 - 20*x^6) + E^30*(500*x + 480*x^3 + 64*x^5 + 5*x^7))/(4*x^5 -
4*E^15*x^6 + E^30*x^7),x]

[Out]

(-2*x^4*(1 + 5*x) + E^15*(-100 - 160*x^2 - 64*x^4 + 5*x^6))/(x^4*(-2 + E^15*x))

Maple [A] (verified)

Time = 0.14 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.34

method	result	size
risch	\(5 x +\frac {\left (-64 \,{\mathrm e}^{15}-2\right ) x^{4}-160 x^{2} {\mathrm e}^{15}-100 \,{\mathrm e}^{15}}{x^{4} \left (x \,{\mathrm e}^{15}-2\right )}\)	\(39\)
norman	\(\frac {5 \,{\mathrm e}^{15} x^{6}+\left (-32 \,{\mathrm e}^{30}-{\mathrm e}^{15}-10\right ) x^{5}-160 x^{2} {\mathrm e}^{15}-100 \,{\mathrm e}^{15}}{x^{4} \left (x \,{\mathrm e}^{15}-2\right )}\)	\(58\)
gosper	\(-\frac {32 x^{5} {\mathrm e}^{30}-5 \,{\mathrm e}^{15} x^{6}+x^{5} {\mathrm e}^{15}+160 x^{2} {\mathrm e}^{15}+10 x^{5}+100 \,{\mathrm e}^{15}}{x^{4} \left (x \,{\mathrm e}^{15}-2\right )}\)	\(63\)
parallelrisch	\(-\frac {64 x^{5} {\mathrm e}^{30}-10 \,{\mathrm e}^{15} x^{6}+2 x^{5} {\mathrm e}^{15}+320 x^{2} {\mathrm e}^{15}+20 x^{5}+200 \,{\mathrm e}^{15}}{2 x^{4} \left (x \,{\mathrm e}^{15}-2\right )}\)	\(64\)

[In]

int(((5*x^7+64*x^5+480*x^3+500*x)*exp(5)^6+(-20*x^6+2*x^5-640*x^2-800)*exp(5)^3+20*x^5)/(x^7*exp(5)^6-4*x^6*ex
p(5)^3+4*x^5),x,method=_RETURNVERBOSE)

[Out]

5*x+((-64*exp(15)-2)*x^4-160*x^2*exp(15)-100*exp(15))/x^4/(x*exp(15)-2)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.66 \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=-\frac {10 \, x^{5} + 2 \, x^{4} - {\left (5 \, x^{6} - 64 \, x^{4} - 160 \, x^{2} - 100\right )} e^{15}}{x^{5} e^{15} - 2 \, x^{4}} \]

[In]

integrate(((5*x^7+64*x^5+480*x^3+500*x)*exp(5)^6+(-20*x^6+2*x^5-640*x^2-800)*exp(5)^3+20*x^5)/(x^7*exp(5)^6-4*
x^6*exp(5)^3+4*x^5),x, algorithm="fricas")

[Out]

-(10*x^5 + 2*x^4 - (5*x^6 - 64*x^4 - 160*x^2 - 100)*e^15)/(x^5*e^15 - 2*x^4)

Sympy [A] (verification not implemented)

Time = 1.73 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.34 \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=5 x + \frac {x^{4} \left (- 64 e^{15} - 2\right ) - 160 x^{2} e^{15} - 100 e^{15}}{x^{5} e^{15} - 2 x^{4}} \]

[In]

integrate(((5*x**7+64*x**5+480*x**3+500*x)*exp(5)**6+(-20*x**6+2*x**5-640*x**2-800)*exp(5)**3+20*x**5)/(x**7*e
xp(5)**6-4*x**6*exp(5)**3+4*x**5),x)

[Out]

5*x + (x**4*(-64*exp(15) - 2) - 160*x**2*exp(15) - 100*exp(15))/(x**5*exp(15) - 2*x**4)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.45 \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=5 \, x - \frac {2 \, {\left (x^{4} {\left (32 \, e^{15} + 1\right )} + 80 \, x^{2} e^{15} + 50 \, e^{15}\right )}}{x^{5} e^{15} - 2 \, x^{4}} \]

[In]

integrate(((5*x^7+64*x^5+480*x^3+500*x)*exp(5)^6+(-20*x^6+2*x^5-640*x^2-800)*exp(5)^3+20*x^5)/(x^7*exp(5)^6-4*
x^6*exp(5)^3+4*x^5),x, algorithm="maxima")

[Out]

5*x - 2*(x^4*(32*e^15 + 1) + 80*x^2*e^15 + 50*e^15)/(x^5*e^15 - 2*x^4)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (27) = 54\).

Time = 0.26 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.45 \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=5 \, x - \frac {25 \, e^{75} + 160 \, e^{45} + 256 \, e^{15} + 8}{4 \, {\left (x e^{15} - 2\right )}} + \frac {5 \, {\left (5 \, x^{3} e^{60} + 32 \, x^{3} e^{30} + 10 \, x^{2} e^{45} + 64 \, x^{2} e^{15} + 20 \, x e^{30} + 40 \, e^{15}\right )}}{4 \, x^{4}} \]

[In]

integrate(((5*x^7+64*x^5+480*x^3+500*x)*exp(5)^6+(-20*x^6+2*x^5-640*x^2-800)*exp(5)^3+20*x^5)/(x^7*exp(5)^6-4*
x^6*exp(5)^3+4*x^5),x, algorithm="giac")

[Out]

5*x - 1/4*(25*e^75 + 160*e^45 + 256*e^15 + 8)/(x*e^15 - 2) + 5/4*(5*x^3*e^60 + 32*x^3*e^30 + 10*x^2*e^45 + 64*
x^2*e^15 + 20*x*e^30 + 40*e^15)/x^4

Mupad [B] (verification not implemented)

Time = 0.23 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.34 \[ \int \frac {20 x^5+e^{15} \left (-800-640 x^2+2 x^5-20 x^6\right )+e^{30} \left (500 x+480 x^3+64 x^5+5 x^7\right )}{4 x^5-4 e^{15} x^6+e^{30} x^7} \, dx=5\,x-\frac {\left (64\,{\mathrm {e}}^{15}+2\right )\,x^4+160\,{\mathrm {e}}^{15}\,x^2+100\,{\mathrm {e}}^{15}}{x^4\,\left (x\,{\mathrm {e}}^{15}-2\right )} \]

[In]

int((exp(30)*(500*x + 480*x^3 + 64*x^5 + 5*x^7) - exp(15)*(640*x^2 - 2*x^5 + 20*x^6 + 800) + 20*x^5)/(x^7*exp(
30) - 4*x^6*exp(15) + 4*x^5),x)

[Out]

5*x - (100*exp(15) + x^4*(64*exp(15) + 2) + 160*x^2*exp(15))/(x^4*(x*exp(15) - 2))