3.63.16 \(\int \frac {180+90 x^2+360 e x^2-90 e^6 x^2+30 x^3-90 e^2 x^3}{144+1152 x+2160 x^2+9 e^{20} x^2-600 x^3-60 x^4+12 x^5-144 e^3 x^5+x^6+9 e^4 x^6+e^{15} (-144 x^2+36 e x^3)+e^{10} (72 x+864 x^2-36 x^3-432 e x^3-6 x^4+54 e^2 x^4)+e (-576 x^2-2304 x^3+288 x^4+48 x^5)+e^2 (72 x^3+864 x^4-36 x^5-6 x^6)+e^5 (-576 x-2304 x^2+288 x^3+48 x^4-432 e^2 x^4+36 e^3 x^5+e (144 x^2+1728 x^3-72 x^4-12 x^5))} \, dx\)

Optimal. Leaf size=31 \[ \frac {5}{-2 x+\left (-4+e^5+e x\right )^2+\frac {4-\frac {x^3}{3}}{x}} \]

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Rubi [F]  time = 180.01, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(180 + 90*x^2 + 360*E*x^2 - 90*E^6*x^2 + 30*x^3 - 90*E^2*x^3)/(144 + 1152*x + 2160*x^2 + 9*E^20*x^2 - 600*
x^3 - 60*x^4 + 12*x^5 - 144*E^3*x^5 + x^6 + 9*E^4*x^6 + E^15*(-144*x^2 + 36*E*x^3) + E^10*(72*x + 864*x^2 - 36
*x^3 - 432*E*x^3 - 6*x^4 + 54*E^2*x^4) + E*(-576*x^2 - 2304*x^3 + 288*x^4 + 48*x^5) + E^2*(72*x^3 + 864*x^4 -
36*x^5 - 6*x^6) + E^5*(-576*x - 2304*x^2 + 288*x^3 + 48*x^4 - 432*E^2*x^4 + 36*E^3*x^5 + E*(144*x^2 + 1728*x^3
- 72*x^4 - 12*x^5))),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.06, size = 41, normalized size = 1.32 \begin {gather*} \frac {15 x}{12+3 \left (-4+e^5\right )^2 x+6 \left (-1-4 e+e^6\right ) x^2+\left (-1+3 e^2\right ) x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(180 + 90*x^2 + 360*E*x^2 - 90*E^6*x^2 + 30*x^3 - 90*E^2*x^3)/(144 + 1152*x + 2160*x^2 + 9*E^20*x^2
- 600*x^3 - 60*x^4 + 12*x^5 - 144*E^3*x^5 + x^6 + 9*E^4*x^6 + E^15*(-144*x^2 + 36*E*x^3) + E^10*(72*x + 864*x^
2 - 36*x^3 - 432*E*x^3 - 6*x^4 + 54*E^2*x^4) + E*(-576*x^2 - 2304*x^3 + 288*x^4 + 48*x^5) + E^2*(72*x^3 + 864*
x^4 - 36*x^5 - 6*x^6) + E^5*(-576*x - 2304*x^2 + 288*x^3 + 48*x^4 - 432*E^2*x^4 + 36*E^3*x^5 + E*(144*x^2 + 17
28*x^3 - 72*x^4 - 12*x^5))),x]

[Out]

(15*x)/(12 + 3*(-4 + E^5)^2*x + 6*(-1 - 4*E + E^6)*x^2 + (-1 + 3*E^2)*x^3)

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fricas [A]  time = 0.72, size = 51, normalized size = 1.65 \begin {gather*} \frac {15 \, x}{3 \, x^{3} e^{2} - x^{3} + 6 \, x^{2} e^{6} - 24 \, x^{2} e - 6 \, x^{2} + 3 \, x e^{10} - 24 \, x e^{5} + 48 \, x + 12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-90*x^2*exp(1)*exp(5)-90*x^3*exp(1)^2+360*x^2*exp(1)+30*x^3+90*x^2+180)/(9*x^2*exp(5)^4+(36*x^3*exp
(1)-144*x^2)*exp(5)^3+(54*x^4*exp(1)^2-432*x^3*exp(1)-6*x^4-36*x^3+864*x^2+72*x)*exp(5)^2+(36*x^5*exp(1)^3-432
*x^4*exp(1)^2+(-12*x^5-72*x^4+1728*x^3+144*x^2)*exp(1)+48*x^4+288*x^3-2304*x^2-576*x)*exp(5)+9*x^6*exp(1)^4-14
4*x^5*exp(1)^3+(-6*x^6-36*x^5+864*x^4+72*x^3)*exp(1)^2+(48*x^5+288*x^4-2304*x^3-576*x^2)*exp(1)+x^6+12*x^5-60*
x^4-600*x^3+2160*x^2+1152*x+144),x, algorithm="fricas")

[Out]

15*x/(3*x^3*e^2 - x^3 + 6*x^2*e^6 - 24*x^2*e - 6*x^2 + 3*x*e^10 - 24*x*e^5 + 48*x + 12)

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-90*x^2*exp(1)*exp(5)-90*x^3*exp(1)^2+360*x^2*exp(1)+30*x^3+90*x^2+180)/(9*x^2*exp(5)^4+(36*x^3*exp
(1)-144*x^2)*exp(5)^3+(54*x^4*exp(1)^2-432*x^3*exp(1)-6*x^4-36*x^3+864*x^2+72*x)*exp(5)^2+(36*x^5*exp(1)^3-432
*x^4*exp(1)^2+(-12*x^5-72*x^4+1728*x^3+144*x^2)*exp(1)+48*x^4+288*x^3-2304*x^2-576*x)*exp(5)+9*x^6*exp(1)^4-14
4*x^5*exp(1)^3+(-6*x^6-36*x^5+864*x^4+72*x^3)*exp(1)^2+(48*x^5+288*x^4-2304*x^3-576*x^2)*exp(1)+x^6+12*x^5-60*
x^4-600*x^3+2160*x^2+1152*x+144),x, algorithm="giac")

[Out]

Timed out

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maple [A]  time = 1.04, size = 50, normalized size = 1.61

method	result	size
risch	\(\frac {5 x}{x \,{\mathrm e}^{10}+2 x^{2} {\mathrm e}^{6}-8 x \,{\mathrm e}^{5}+x^{3} {\mathrm e}^{2}-8 x^{2} {\mathrm e}-\frac {x^{3}}{3}-2 x^{2}+16 x +4}\)	\(50\)
gosper	\(\frac {15 x}{3 x^{3} {\mathrm e}^{2}+6 x^{2} {\mathrm e} \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-24 x^{2} {\mathrm e}-x^{3}-24 x \,{\mathrm e}^{5}-6 x^{2}+48 x +12}\)	\(58\)
norman	\(\frac {15 x}{3 x^{3} {\mathrm e}^{2}+6 x^{2} {\mathrm e} \,{\mathrm e}^{5}+3 x \,{\mathrm e}^{10}-24 x^{2} {\mathrm e}-x^{3}-24 x \,{\mathrm e}^{5}-6 x^{2}+48 x +12}\)	\(58\)
default	\(5 \left (\munderset {\textit {\_R} =\RootOf \left (-144-\left (1-6 \,{\mathrm e}^{2}+9 \,{\mathrm e}^{4}\right ) \textit {\_Z}^{6}-\left (-36 \,{\mathrm e}^{2}+36 \,{\mathrm e}^{8}-12 \,{\mathrm e}^{6}+48 \,{\mathrm e}-144 \,{\mathrm e}^{3}+12\right ) \textit {\_Z}^{5}-\left (48 \,{\mathrm e}^{5}+864 \,{\mathrm e}^{2}-6 \,{\mathrm e}^{10}-72 \,{\mathrm e}^{6}-432 \,{\mathrm e}^{7}+54 \,{\mathrm e}^{12}+288 \,{\mathrm e}-60\right ) \textit {\_Z}^{4}-\left (288 \,{\mathrm e}^{5}+72 \,{\mathrm e}^{2}-36 \,{\mathrm e}^{10}+1728 \,{\mathrm e}^{6}+36 \,{\mathrm e}^{16}-432 \,{\mathrm e}^{11}-2304 \,{\mathrm e}-600\right ) \textit {\_Z}^{3}-\left (-2304 \,{\mathrm e}^{5}+864 \,{\mathrm e}^{10}+9 \,{\mathrm e}^{20}+144 \,{\mathrm e}^{6}-144 \,{\mathrm e}^{15}-576 \,{\mathrm e}+2160\right ) \textit {\_Z}^{2}-\left (-576 \,{\mathrm e}^{5}+72 \,{\mathrm e}^{10}+1152\right ) \textit {\_Z} \right )}{\sum }\frac {\left (6+\left (-3 \,{\mathrm e}^{2}+1\right ) \textit {\_R}^{3}+3 \left (1-{\mathrm e}^{6}+4 \,{\mathrm e}\right ) \textit {\_R}^{2}\right ) \ln \left (x -\textit {\_R} \right )}{192+720 \textit {\_R} +12 \,{\mathrm e}^{10}-96 \,{\mathrm e}^{5}+576 \textit {\_R}^{3} {\mathrm e}^{2}+40 \textit {\_R}^{4} {\mathrm e}-10 \textit {\_R}^{4} {\mathrm e}^{6}-120 \textit {\_R}^{4} {\mathrm e}^{3}-48 \textit {\_R}^{3} {\mathrm e}^{6}+36 \textit {\_R}^{2} {\mathrm e}^{2}-192 \textit {\_R} \,{\mathrm e}+\textit {\_R}^{5}+10 \textit {\_R}^{4}+144 \textit {\_R}^{2} {\mathrm e}^{5}+288 \textit {\_R} \,{\mathrm e}^{10}-768 \textit {\_R} \,{\mathrm e}^{5}-40 \textit {\_R}^{3}-300 \textit {\_R}^{2}+36 \textit {\_R}^{3} {\mathrm e}^{12}-6 \,{\mathrm e}^{2} \textit {\_R}^{5}-48 \textit {\_R} \,{\mathrm e}^{15}+18 \textit {\_R}^{2} {\mathrm e}^{16}+32 \textit {\_R}^{3} {\mathrm e}^{5}-30 \textit {\_R}^{4} {\mathrm e}^{2}-1152 \textit {\_R}^{2} {\mathrm e}+192 \textit {\_R}^{3} {\mathrm e}-18 \,{\mathrm e}^{10} \textit {\_R}^{2}+3 \textit {\_R} \,{\mathrm e}^{20}-4 \textit {\_R}^{3} {\mathrm e}^{10}+9 \textit {\_R}^{5} {\mathrm e}^{4}+30 \textit {\_R}^{4} {\mathrm e}^{8}-288 \textit {\_R}^{3} {\mathrm e}^{7}-216 \textit {\_R}^{2} {\mathrm e}^{11}+864 \textit {\_R}^{2} {\mathrm e}^{6}+48 \textit {\_R} \,{\mathrm e}^{6}}\right )\)	\(409\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-90*x^2*exp(1)*exp(5)-90*x^3*exp(1)^2+360*x^2*exp(1)+30*x^3+90*x^2+180)/(9*x^2*exp(5)^4+(36*x^3*exp(1)-14
4*x^2)*exp(5)^3+(54*x^4*exp(1)^2-432*x^3*exp(1)-6*x^4-36*x^3+864*x^2+72*x)*exp(5)^2+(36*x^5*exp(1)^3-432*x^4*e
xp(1)^2+(-12*x^5-72*x^4+1728*x^3+144*x^2)*exp(1)+48*x^4+288*x^3-2304*x^2-576*x)*exp(5)+9*x^6*exp(1)^4-144*x^5*
exp(1)^3+(-6*x^6-36*x^5+864*x^4+72*x^3)*exp(1)^2+(48*x^5+288*x^4-2304*x^3-576*x^2)*exp(1)+x^6+12*x^5-60*x^4-60
0*x^3+2160*x^2+1152*x+144),x,method=_RETURNVERBOSE)

[Out]

5*x/(x*exp(10)+2*x^2*exp(6)-8*x*exp(5)+x^3*exp(2)-8*x^2*exp(1)-1/3*x^3-2*x^2+16*x+4)

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maxima [A]  time = 0.36, size = 41, normalized size = 1.32 \begin {gather*} \frac {15 \, x}{x^{3} {\left (3 \, e^{2} - 1\right )} + 6 \, x^{2} {\left (e^{6} - 4 \, e - 1\right )} + 3 \, x {\left (e^{10} - 8 \, e^{5} + 16\right )} + 12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-90*x^2*exp(1)*exp(5)-90*x^3*exp(1)^2+360*x^2*exp(1)+30*x^3+90*x^2+180)/(9*x^2*exp(5)^4+(36*x^3*exp
(1)-144*x^2)*exp(5)^3+(54*x^4*exp(1)^2-432*x^3*exp(1)-6*x^4-36*x^3+864*x^2+72*x)*exp(5)^2+(36*x^5*exp(1)^3-432
*x^4*exp(1)^2+(-12*x^5-72*x^4+1728*x^3+144*x^2)*exp(1)+48*x^4+288*x^3-2304*x^2-576*x)*exp(5)+9*x^6*exp(1)^4-14
4*x^5*exp(1)^3+(-6*x^6-36*x^5+864*x^4+72*x^3)*exp(1)^2+(48*x^5+288*x^4-2304*x^3-576*x^2)*exp(1)+x^6+12*x^5-60*
x^4-600*x^3+2160*x^2+1152*x+144),x, algorithm="maxima")

[Out]

15*x/(x^3*(3*e^2 - 1) + 6*x^2*(e^6 - 4*e - 1) + 3*x*(e^10 - 8*e^5 + 16) + 12)

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mupad [B]  time = 4.48, size = 44, normalized size = 1.42 \begin {gather*} \frac {15\,x}{\left (3\,{\mathrm {e}}^2-1\right )\,x^3+\left (6\,{\mathrm {e}}^6-24\,\mathrm {e}-6\right )\,x^2+\left (3\,{\mathrm {e}}^{10}-24\,{\mathrm {e}}^5+48\right )\,x+12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((360*x^2*exp(1) - 90*x^3*exp(2) - 90*x^2*exp(6) + 90*x^2 + 30*x^3 + 180)/(1152*x - 144*x^5*exp(3) + 9*x^6*
exp(4) + 9*x^2*exp(20) + 2160*x^2 - 600*x^3 - 60*x^4 + 12*x^5 + x^6 + exp(5)*(36*x^5*exp(3) - 432*x^4*exp(2) -
576*x - 2304*x^2 + 288*x^3 + 48*x^4 + exp(1)*(144*x^2 + 1728*x^3 - 72*x^4 - 12*x^5)) + exp(10)*(72*x - 432*x^
3*exp(1) + 54*x^4*exp(2) + 864*x^2 - 36*x^3 - 6*x^4) + exp(15)*(36*x^3*exp(1) - 144*x^2) + exp(2)*(72*x^3 + 86
4*x^4 - 36*x^5 - 6*x^6) - exp(1)*(576*x^2 + 2304*x^3 - 288*x^4 - 48*x^5) + 144),x)

[Out]

(15*x)/(x^3*(3*exp(2) - 1) - x^2*(24*exp(1) - 6*exp(6) + 6) + x*(3*exp(10) - 24*exp(5) + 48) + 12)

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sympy [A]  time = 15.90, size = 42, normalized size = 1.35 \begin {gather*} \frac {15 x}{x^{3} \left (-1 + 3 e^{2}\right ) + x^{2} \left (- 24 e - 6 + 6 e^{6}\right ) + x \left (- 24 e^{5} + 48 + 3 e^{10}\right ) + 12} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-90*x**2*exp(1)*exp(5)-90*x**3*exp(1)**2+360*x**2*exp(1)+30*x**3+90*x**2+180)/(9*x**2*exp(5)**4+(36
*x**3*exp(1)-144*x**2)*exp(5)**3+(54*x**4*exp(1)**2-432*x**3*exp(1)-6*x**4-36*x**3+864*x**2+72*x)*exp(5)**2+(3
6*x**5*exp(1)**3-432*x**4*exp(1)**2+(-12*x**5-72*x**4+1728*x**3+144*x**2)*exp(1)+48*x**4+288*x**3-2304*x**2-57
6*x)*exp(5)+9*x**6*exp(1)**4-144*x**5*exp(1)**3+(-6*x**6-36*x**5+864*x**4+72*x**3)*exp(1)**2+(48*x**5+288*x**4
-2304*x**3-576*x**2)*exp(1)+x**6+12*x**5-60*x**4-600*x**3+2160*x**2+1152*x+144),x)

[Out]

15*x/(x**3*(-1 + 3*exp(2)) + x**2*(-24*E - 6 + 6*exp(6)) + x*(-24*exp(5) + 48 + 3*exp(10)) + 12)

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