3.30.49 \(\int \frac {1}{25} (-4920+17048 x-14760 x^2+3600 x^3+e^{10} (800 x-960 x^2+256 x^3)+e^5 (-1200+7520 x-7536 x^2+1920 x^3)) \, dx\)

Optimal. Leaf size=24 \[ \left (x+\left (-\frac {2}{5}+\frac {1}{x}\right ) x \left (6+x-4 \left (4+e^5\right ) x\right )\right )^2 \]

________________________________________________________________________________________

Rubi [B]  time = 0.03, antiderivative size = 89, normalized size of antiderivative = 3.71, number of steps used = 4, number of rules used = 1, integrand size = 56, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {12} \begin {gather*} \frac {64 e^{10} x^4}{25}+\frac {96 e^5 x^4}{5}+36 x^4-\frac {64 e^{10} x^3}{5}-\frac {2512 e^5 x^3}{25}-\frac {984 x^3}{5}+16 e^{10} x^2+\frac {752 e^5 x^2}{5}+\frac {8524 x^2}{25}-48 e^5 x-\frac {984 x}{5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-4920 + 17048*x - 14760*x^2 + 3600*x^3 + E^10*(800*x - 960*x^2 + 256*x^3) + E^5*(-1200 + 7520*x - 7536*x^
2 + 1920*x^3))/25,x]

[Out]

(-984*x)/5 - 48*E^5*x + (8524*x^2)/25 + (752*E^5*x^2)/5 + 16*E^10*x^2 - (984*x^3)/5 - (2512*E^5*x^3)/25 - (64*
E^10*x^3)/5 + 36*x^4 + (96*E^5*x^4)/5 + (64*E^10*x^4)/25

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int \left (-4920+17048 x-14760 x^2+3600 x^3+e^{10} \left (800 x-960 x^2+256 x^3\right )+e^5 \left (-1200+7520 x-7536 x^2+1920 x^3\right )\right ) \, dx\\ &=-\frac {984 x}{5}+\frac {8524 x^2}{25}-\frac {984 x^3}{5}+36 x^4+\frac {1}{25} e^5 \int \left (-1200+7520 x-7536 x^2+1920 x^3\right ) \, dx+\frac {1}{25} e^{10} \int \left (800 x-960 x^2+256 x^3\right ) \, dx\\ &=-\frac {984 x}{5}-48 e^5 x+\frac {8524 x^2}{25}+\frac {752 e^5 x^2}{5}+16 e^{10} x^2-\frac {984 x^3}{5}-\frac {2512 e^5 x^3}{25}-\frac {64 e^{10} x^3}{5}+36 x^4+\frac {96 e^5 x^4}{5}+\frac {64 e^{10} x^4}{25}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.01, size = 81, normalized size = 3.38 \begin {gather*} \frac {8}{25} \left (-615 x-150 e^5 x+\frac {2131 x^2}{2}+470 e^5 x^2+50 e^{10} x^2-615 x^3-314 e^5 x^3-40 e^{10} x^3+\frac {225 x^4}{2}+60 e^5 x^4+8 e^{10} x^4\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-4920 + 17048*x - 14760*x^2 + 3600*x^3 + E^10*(800*x - 960*x^2 + 256*x^3) + E^5*(-1200 + 7520*x - 7
536*x^2 + 1920*x^3))/25,x]

[Out]

(8*(-615*x - 150*E^5*x + (2131*x^2)/2 + 470*E^5*x^2 + 50*E^10*x^2 - 615*x^3 - 314*E^5*x^3 - 40*E^10*x^3 + (225
*x^4)/2 + 60*E^5*x^4 + 8*E^10*x^4))/25

________________________________________________________________________________________

fricas [B]  time = 0.77, size = 62, normalized size = 2.58 \begin {gather*} 36 \, x^{4} - \frac {984}{5} \, x^{3} + \frac {8524}{25} \, x^{2} + \frac {16}{25} \, {\left (4 \, x^{4} - 20 \, x^{3} + 25 \, x^{2}\right )} e^{10} + \frac {16}{25} \, {\left (30 \, x^{4} - 157 \, x^{3} + 235 \, x^{2} - 75 \, x\right )} e^{5} - \frac {984}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(256*x^3-960*x^2+800*x)*exp(5)^2+1/25*(1920*x^3-7536*x^2+7520*x-1200)*exp(5)+144*x^3-2952/5*x^2
+17048/25*x-984/5,x, algorithm="fricas")

[Out]

36*x^4 - 984/5*x^3 + 8524/25*x^2 + 16/25*(4*x^4 - 20*x^3 + 25*x^2)*e^10 + 16/25*(30*x^4 - 157*x^3 + 235*x^2 -
75*x)*e^5 - 984/5*x

________________________________________________________________________________________

giac [B]  time = 0.20, size = 62, normalized size = 2.58 \begin {gather*} 36 \, x^{4} - \frac {984}{5} \, x^{3} + \frac {8524}{25} \, x^{2} + \frac {16}{25} \, {\left (4 \, x^{4} - 20 \, x^{3} + 25 \, x^{2}\right )} e^{10} + \frac {16}{25} \, {\left (30 \, x^{4} - 157 \, x^{3} + 235 \, x^{2} - 75 \, x\right )} e^{5} - \frac {984}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(256*x^3-960*x^2+800*x)*exp(5)^2+1/25*(1920*x^3-7536*x^2+7520*x-1200)*exp(5)+144*x^3-2952/5*x^2
+17048/25*x-984/5,x, algorithm="giac")

[Out]

36*x^4 - 984/5*x^3 + 8524/25*x^2 + 16/25*(4*x^4 - 20*x^3 + 25*x^2)*e^10 + 16/25*(30*x^4 - 157*x^3 + 235*x^2 -
75*x)*e^5 - 984/5*x

________________________________________________________________________________________

maple [B]  time = 0.03, size = 58, normalized size = 2.42

method	result	size
norman	\(\left (-48 \,{\mathrm e}^{5}-\frac {984}{5}\right ) x +\left (16 \,{\mathrm e}^{10}+\frac {752 \,{\mathrm e}^{5}}{5}+\frac {8524}{25}\right ) x^{2}+\left (-\frac {64 \,{\mathrm e}^{10}}{5}-\frac {2512 \,{\mathrm e}^{5}}{25}-\frac {984}{5}\right ) x^{3}+\left (\frac {64 \,{\mathrm e}^{10}}{25}+\frac {96 \,{\mathrm e}^{5}}{5}+36\right ) x^{4}\)	\(58\)
default	\(\frac {{\mathrm e}^{10} \left (64 x^{4}-320 x^{3}+400 x^{2}\right )}{25}+\frac {{\mathrm e}^{5} \left (480 x^{4}-2512 x^{3}+3760 x^{2}-1200 x \right )}{25}+36 x^{4}-\frac {984 x^{3}}{5}+\frac {8524 x^{2}}{25}-\frac {984 x}{5}\)	\(65\)
gosper	\(\frac {4 x \left (16 x^{3} {\mathrm e}^{10}-80 x^{2} {\mathrm e}^{10}+120 x^{3} {\mathrm e}^{5}+100 x \,{\mathrm e}^{10}-628 x^{2} {\mathrm e}^{5}+225 x^{3}+940 x \,{\mathrm e}^{5}-1230 x^{2}-300 \,{\mathrm e}^{5}+2131 x -1230\right )}{25}\)	\(67\)
risch	\(\frac {64 x^{4} {\mathrm e}^{10}}{25}-\frac {64 x^{3} {\mathrm e}^{10}}{5}+16 x^{2} {\mathrm e}^{10}+\frac {96 x^{4} {\mathrm e}^{5}}{5}-\frac {2512 x^{3} {\mathrm e}^{5}}{25}+\frac {752 x^{2} {\mathrm e}^{5}}{5}-48 x \,{\mathrm e}^{5}+36 x^{4}-\frac {984 x^{3}}{5}+\frac {8524 x^{2}}{25}-\frac {984 x}{5}\)	\(67\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/25*(256*x^3-960*x^2+800*x)*exp(5)^2+1/25*(1920*x^3-7536*x^2+7520*x-1200)*exp(5)+144*x^3-2952/5*x^2+17048
/25*x-984/5,x,method=_RETURNVERBOSE)

[Out]

(-48*exp(5)-984/5)*x+(16*exp(5)^2+752/5*exp(5)+8524/25)*x^2+(-64/5*exp(5)^2-2512/25*exp(5)-984/5)*x^3+(64/25*e
xp(5)^2+96/5*exp(5)+36)*x^4

________________________________________________________________________________________

maxima [B]  time = 0.36, size = 62, normalized size = 2.58 \begin {gather*} 36 \, x^{4} - \frac {984}{5} \, x^{3} + \frac {8524}{25} \, x^{2} + \frac {16}{25} \, {\left (4 \, x^{4} - 20 \, x^{3} + 25 \, x^{2}\right )} e^{10} + \frac {16}{25} \, {\left (30 \, x^{4} - 157 \, x^{3} + 235 \, x^{2} - 75 \, x\right )} e^{5} - \frac {984}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(256*x^3-960*x^2+800*x)*exp(5)^2+1/25*(1920*x^3-7536*x^2+7520*x-1200)*exp(5)+144*x^3-2952/5*x^2
+17048/25*x-984/5,x, algorithm="maxima")

[Out]

36*x^4 - 984/5*x^3 + 8524/25*x^2 + 16/25*(4*x^4 - 20*x^3 + 25*x^2)*e^10 + 16/25*(30*x^4 - 157*x^3 + 235*x^2 -
75*x)*e^5 - 984/5*x

________________________________________________________________________________________

mupad [B]  time = 0.07, size = 53, normalized size = 2.21 \begin {gather*} \left (\frac {96\,{\mathrm {e}}^5}{5}+\frac {64\,{\mathrm {e}}^{10}}{25}+36\right )\,x^4+\left (-\frac {2512\,{\mathrm {e}}^5}{25}-\frac {64\,{\mathrm {e}}^{10}}{5}-\frac {984}{5}\right )\,x^3+\left (\frac {752\,{\mathrm {e}}^5}{5}+16\,{\mathrm {e}}^{10}+\frac {8524}{25}\right )\,x^2+\left (-48\,{\mathrm {e}}^5-\frac {984}{5}\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((17048*x)/25 + (exp(10)*(800*x - 960*x^2 + 256*x^3))/25 + (exp(5)*(7520*x - 7536*x^2 + 1920*x^3 - 1200))/2
5 - (2952*x^2)/5 + 144*x^3 - 984/5,x)

[Out]

x^4*((96*exp(5))/5 + (64*exp(10))/25 + 36) - x^3*((2512*exp(5))/25 + (64*exp(10))/5 + 984/5) + x^2*((752*exp(5
))/5 + 16*exp(10) + 8524/25) - x*(48*exp(5) + 984/5)

________________________________________________________________________________________

sympy [B]  time = 0.08, size = 70, normalized size = 2.92 \begin {gather*} x^{4} \left (36 + \frac {96 e^{5}}{5} + \frac {64 e^{10}}{25}\right ) + x^{3} \left (- \frac {64 e^{10}}{5} - \frac {2512 e^{5}}{25} - \frac {984}{5}\right ) + x^{2} \left (\frac {8524}{25} + \frac {752 e^{5}}{5} + 16 e^{10}\right ) + x \left (- 48 e^{5} - \frac {984}{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/25*(256*x**3-960*x**2+800*x)*exp(5)**2+1/25*(1920*x**3-7536*x**2+7520*x-1200)*exp(5)+144*x**3-2952
/5*x**2+17048/25*x-984/5,x)

[Out]

x**4*(36 + 96*exp(5)/5 + 64*exp(10)/25) + x**3*(-64*exp(10)/5 - 2512*exp(5)/25 - 984/5) + x**2*(8524/25 + 752*
exp(5)/5 + 16*exp(10)) + x*(-48*exp(5) - 984/5)

________________________________________________________________________________________