3.39.98 \(\int \frac {5 x^4+10 x^5+e^{4 x} (5+10 x)+e^{10} (42+90 x)+e^5 (31 x^2+60 x^3)+e^{2 x} (42+e^5 (-58-122 x)+90 x-10 x^2-20 x^3+e^{10} (5+10 x))+e^{3 x} (-29-61 x+e^5 (10+20 x))+e^x (e^{10} (-29-61 x)+31 x^2+59 x^3+e^5 (84+180 x-10 x^2-20 x^3))+(45 e^{10}+5 e^{4 x}+e^{3 x} (-30+10 e^5)+30 e^5 x^2+5 x^4+e^{2 x} (45-60 e^5+5 e^{10}-10 x^2)+e^x (-30 e^{10}+30 x^2+e^5 (90-10 x^2))) \log (2 x)}{9 e^{10}+e^{4 x}+e^{3 x} (-6+2 e^5)+6 e^5 x^2+x^4+e^{2 x} (9-12 e^5+e^{10}-2 x^2)+e^x (-6 e^{10}+6 x^2+e^5 (18-2 x^2))} \, dx\)

Optimal. Leaf size=35 \[ -\frac {x}{3-e^x+\frac {x^2}{e^5+e^x}}+5 x (x+\log (2 x)) \]

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Rubi [F]  time = 7.96, 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 {5 x^4+10 x^5+e^{4 x} (5+10 x)+e^{10} (42+90 x)+e^5 \left (31 x^2+60 x^3\right )+e^{2 x} \left (42+e^5 (-58-122 x)+90 x-10 x^2-20 x^3+e^{10} (5+10 x)\right )+e^{3 x} \left (-29-61 x+e^5 (10+20 x)\right )+e^x \left (e^{10} (-29-61 x)+31 x^2+59 x^3+e^5 \left (84+180 x-10 x^2-20 x^3\right )\right )+\left (45 e^{10}+5 e^{4 x}+e^{3 x} \left (-30+10 e^5\right )+30 e^5 x^2+5 x^4+e^{2 x} \left (45-60 e^5+5 e^{10}-10 x^2\right )+e^x \left (-30 e^{10}+30 x^2+e^5 \left (90-10 x^2\right )\right )\right ) \log (2 x)}{9 e^{10}+e^{4 x}+e^{3 x} \left (-6+2 e^5\right )+6 e^5 x^2+x^4+e^{2 x} \left (9-12 e^5+e^{10}-2 x^2\right )+e^x \left (-6 e^{10}+6 x^2+e^5 \left (18-2 x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(5*x^4 + 10*x^5 + E^(4*x)*(5 + 10*x) + E^10*(42 + 90*x) + E^5*(31*x^2 + 60*x^3) + E^(2*x)*(42 + E^5*(-58 -
122*x) + 90*x - 10*x^2 - 20*x^3 + E^10*(5 + 10*x)) + E^(3*x)*(-29 - 61*x + E^5*(10 + 20*x)) + E^x*(E^10*(-29
- 61*x) + 31*x^2 + 59*x^3 + E^5*(84 + 180*x - 10*x^2 - 20*x^3)) + (45*E^10 + 5*E^(4*x) + E^(3*x)*(-30 + 10*E^5
) + 30*E^5*x^2 + 5*x^4 + E^(2*x)*(45 - 60*E^5 + 5*E^10 - 10*x^2) + E^x*(-30*E^10 + 30*x^2 + E^5*(90 - 10*x^2))
)*Log[2*x])/(9*E^10 + E^(4*x) + E^(3*x)*(-6 + 2*E^5) + 6*E^5*x^2 + x^4 + E^(2*x)*(9 - 12*E^5 + E^10 - 2*x^2) +
E^x*(-6*E^10 + 6*x^2 + E^5*(18 - 2*x^2))),x]

[Out]

5*x^2 + 5*x*Log[2*x] + E^5*Defer[Int][(-3*E^5 + E^(2*x) - 3*E^x*(1 - E^5/3) - x^2)^(-1), x] + Defer[Int][E^x/(
-3*E^5 + E^(2*x) - 3*E^x*(1 - E^5/3) - x^2), x] - 3*E^5*(3 + E^5)*Defer[Int][x/(3*E^5 - E^(2*x) + 3*E^x*(1 - E
^5/3) + x^2)^2, x] - 3*(3 + E^5)*Defer[Int][(E^x*x)/(3*E^5 - E^(2*x) + 3*E^x*(1 - E^5/3) + x^2)^2, x] + 2*E^5*
Defer[Int][x^2/(3*E^5 - E^(2*x) + 3*E^x*(1 - E^5/3) + x^2)^2, x] + 2*Defer[Int][(E^x*x^2)/(3*E^5 - E^(2*x) + 3
*E^x*(1 - E^5/3) + x^2)^2, x] - (3 + E^5)*Defer[Int][x^3/(3*E^5 - E^(2*x) + 3*E^x*(1 - E^5/3) + x^2)^2, x] - 2
*Defer[Int][(E^x*x^3)/(3*E^5 - E^(2*x) + 3*E^x*(1 - E^5/3) + x^2)^2, x] + (3 + E^5)*Defer[Int][x/(3*E^5 - E^(2
*x) + 3*E^x*(1 - E^5/3) + x^2), x] + Defer[Int][(E^x*x)/(3*E^5 - E^(2*x) + 3*E^x*(1 - E^5/3) + x^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 e^{4 x} (1+2 x)+5 e^{2 (5+x)} (1+2 x)+10 e^{5+3 x} (1+2 x)+5 x^4 (1+2 x)+6 e^{10} (7+15 x)+e^x x^2 (31+59 x)+e^5 x^2 (31+60 x)-e^{3 x} (29+61 x)-e^{10+x} (29+61 x)-2 e^{5+2 x} (29+61 x)+e^{2 x} \left (42+90 x-10 x^2-20 x^3\right )-2 e^{5+x} \left (-42-90 x+5 x^2+10 x^3\right )+5 \left (-3 e^5-3 e^x+e^{2 x}+e^{5+x}-x^2\right )^2 \log (2 x)}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx\\ &=\int \left (\frac {-e^5-e^x+e^x x+3 \left (1+\frac {e^5}{3}\right ) x}{3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2}+\frac {x \left (-9 e^5 \left (1+\frac {e^5}{3}\right )-9 e^x \left (1+\frac {e^5}{3}\right )+2 e^5 x+2 e^x x-2 e^x x^2-3 \left (1+\frac {e^5}{3}\right ) x^2\right )}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2}+5 (1+2 x+\log (2 x))\right ) \, dx\\ &=5 \int (1+2 x+\log (2 x)) \, dx+\int \frac {-e^5-e^x+e^x x+3 \left (1+\frac {e^5}{3}\right ) x}{3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2} \, dx+\int \frac {x \left (-9 e^5 \left (1+\frac {e^5}{3}\right )-9 e^x \left (1+\frac {e^5}{3}\right )+2 e^5 x+2 e^x x-2 e^x x^2-3 \left (1+\frac {e^5}{3}\right ) x^2\right )}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx\\ &=5 x+5 x^2+5 \int \log (2 x) \, dx+\int \frac {e^5 (-1+x)+e^x (-1+x)+3 x}{3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2} \, dx+\int \frac {x \left (-3 e^{10}-3 e^{5+x}-3 x^2-e^5 \left (9-2 x+x^2\right )-e^x \left (9-2 x+2 x^2\right )\right )}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx\\ &=5 x^2+5 x \log (2 x)+\int \left (-\frac {9 e^5 \left (1+\frac {e^5}{3}\right ) x}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2}-\frac {9 e^x \left (1+\frac {e^5}{3}\right ) x}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2}+\frac {2 e^5 x^2}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2}+\frac {2 e^x x^2}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2}-\frac {2 e^x x^3}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2}-\frac {3 \left (1+\frac {e^5}{3}\right ) x^3}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2}\right ) \, dx+\int \left (\frac {e^5}{-3 e^5+e^{2 x}-3 e^x \left (1-\frac {e^5}{3}\right )-x^2}+\frac {e^x}{-3 e^5+e^{2 x}-3 e^x \left (1-\frac {e^5}{3}\right )-x^2}+\frac {e^x x}{3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2}+\frac {3 \left (1+\frac {e^5}{3}\right ) x}{3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2}\right ) \, dx\\ &=5 x^2+5 x \log (2 x)+2 \int \frac {e^x x^2}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx-2 \int \frac {e^x x^3}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx+e^5 \int \frac {1}{-3 e^5+e^{2 x}-3 e^x \left (1-\frac {e^5}{3}\right )-x^2} \, dx+\left (2 e^5\right ) \int \frac {x^2}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx-\left (3+e^5\right ) \int \frac {x^3}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx+\left (3+e^5\right ) \int \frac {x}{3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2} \, dx-\left (3 \left (3+e^5\right )\right ) \int \frac {e^x x}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx-\left (3 e^5 \left (3+e^5\right )\right ) \int \frac {x}{\left (3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2\right )^2} \, dx+\int \frac {e^x}{-3 e^5+e^{2 x}-3 e^x \left (1-\frac {e^5}{3}\right )-x^2} \, dx+\int \frac {e^x x}{3 e^5-e^{2 x}+3 e^x \left (1-\frac {e^5}{3}\right )+x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.28, size = 50, normalized size = 1.43 \begin {gather*} 5 x^2+\frac {\left (e^5+e^x\right ) x}{-3 e^5-3 e^x+e^{2 x}+e^{5+x}-x^2}+5 x \log (2 x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(5*x^4 + 10*x^5 + E^(4*x)*(5 + 10*x) + E^10*(42 + 90*x) + E^5*(31*x^2 + 60*x^3) + E^(2*x)*(42 + E^5*
(-58 - 122*x) + 90*x - 10*x^2 - 20*x^3 + E^10*(5 + 10*x)) + E^(3*x)*(-29 - 61*x + E^5*(10 + 20*x)) + E^x*(E^10
*(-29 - 61*x) + 31*x^2 + 59*x^3 + E^5*(84 + 180*x - 10*x^2 - 20*x^3)) + (45*E^10 + 5*E^(4*x) + E^(3*x)*(-30 +
10*E^5) + 30*E^5*x^2 + 5*x^4 + E^(2*x)*(45 - 60*E^5 + 5*E^10 - 10*x^2) + E^x*(-30*E^10 + 30*x^2 + E^5*(90 - 10
*x^2)))*Log[2*x])/(9*E^10 + E^(4*x) + E^(3*x)*(-6 + 2*E^5) + 6*E^5*x^2 + x^4 + E^(2*x)*(9 - 12*E^5 + E^10 - 2*
x^2) + E^x*(-6*E^10 + 6*x^2 + E^5*(18 - 2*x^2))),x]

[Out]

5*x^2 + ((E^5 + E^x)*x)/(-3*E^5 - 3*E^x + E^(2*x) + E^(5 + x) - x^2) + 5*x*Log[2*x]

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fricas [B]  time = 0.58, size = 104, normalized size = 2.97 \begin {gather*} \frac {5 \, x^{4} - 5 \, x^{2} e^{\left (2 \, x\right )} + {\left (15 \, x^{2} - x\right )} e^{5} - {\left (5 \, x^{2} e^{5} - 15 \, x^{2} + x\right )} e^{x} + 5 \, {\left (x^{3} + 3 \, x e^{5} - x e^{\left (2 \, x\right )} - {\left (x e^{5} - 3 \, x\right )} e^{x}\right )} \log \left (2 \, x\right )}{x^{2} - {\left (e^{5} - 3\right )} e^{x} + 3 \, e^{5} - e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)^4+(10*exp(5)-30)*exp(x)^3+(5*exp(5)^2-60*exp(5)-10*x^2+45)*exp(x)^2+(-30*exp(5)^2+(-10*x^
2+90)*exp(5)+30*x^2)*exp(x)+45*exp(5)^2+30*x^2*exp(5)+5*x^4)*log(2*x)+(10*x+5)*exp(x)^4+((20*x+10)*exp(5)-61*x
-29)*exp(x)^3+((10*x+5)*exp(5)^2+(-122*x-58)*exp(5)-20*x^3-10*x^2+90*x+42)*exp(x)^2+((-61*x-29)*exp(5)^2+(-20*
x^3-10*x^2+180*x+84)*exp(5)+59*x^3+31*x^2)*exp(x)+(90*x+42)*exp(5)^2+(60*x^3+31*x^2)*exp(5)+10*x^5+5*x^4)/(exp
(x)^4+(2*exp(5)-6)*exp(x)^3+(exp(5)^2-12*exp(5)-2*x^2+9)*exp(x)^2+(-6*exp(5)^2+(-2*x^2+18)*exp(5)+6*x^2)*exp(x
)+9*exp(5)^2+6*x^2*exp(5)+x^4),x, algorithm="fricas")

[Out]

(5*x^4 - 5*x^2*e^(2*x) + (15*x^2 - x)*e^5 - (5*x^2*e^5 - 15*x^2 + x)*e^x + 5*(x^3 + 3*x*e^5 - x*e^(2*x) - (x*e
^5 - 3*x)*e^x)*log(2*x))/(x^2 - (e^5 - 3)*e^x + 3*e^5 - e^(2*x))

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giac [B]  time = 4.44, size = 1618, normalized size = 46.23 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)^4+(10*exp(5)-30)*exp(x)^3+(5*exp(5)^2-60*exp(5)-10*x^2+45)*exp(x)^2+(-30*exp(5)^2+(-10*x^
2+90)*exp(5)+30*x^2)*exp(x)+45*exp(5)^2+30*x^2*exp(5)+5*x^4)*log(2*x)+(10*x+5)*exp(x)^4+((20*x+10)*exp(5)-61*x
-29)*exp(x)^3+((10*x+5)*exp(5)^2+(-122*x-58)*exp(5)-20*x^3-10*x^2+90*x+42)*exp(x)^2+((-61*x-29)*exp(5)^2+(-20*
x^3-10*x^2+180*x+84)*exp(5)+59*x^3+31*x^2)*exp(x)+(90*x+42)*exp(5)^2+(60*x^3+31*x^2)*exp(5)+10*x^5+5*x^4)/(exp
(x)^4+(2*exp(5)-6)*exp(x)^3+(exp(5)^2-12*exp(5)-2*x^2+9)*exp(x)^2+(-6*exp(5)^2+(-2*x^2+18)*exp(5)+6*x^2)*exp(x
)+9*exp(5)^2+6*x^2*exp(5)+x^4),x, algorithm="giac")

[Out]

(20*x^8 + 20*x^7*log(2) + 20*x^7*log(x) - 20*x^7 + 5*x^6*e^10 + 150*x^6*e^5 - 20*x^6*e^(2*x) - 20*x^6*e^(x + 5
) + 60*x^6*e^x - 30*x^6*log(2) + 5*x^5*e^10*log(2) + 150*x^5*e^5*log(2) - 20*x^5*e^(2*x)*log(2) - 20*x^5*e^(x
+ 5)*log(2) + 60*x^5*e^x*log(2) - 30*x^6*log(x) + 5*x^5*e^10*log(x) + 150*x^5*e^5*log(x) - 20*x^5*e^(2*x)*log(
x) - 20*x^5*e^(x + 5)*log(x) + 60*x^5*e^x*log(x) + 55*x^6 - 64*x^5*e^5 + 40*x^5*e^(2*x) + 50*x^5*e^(x + 5) - 1
54*x^5*e^x + 55*x^5*log(2) - 5*x^4*e^10*log(2) - 120*x^4*e^5*log(2) + 40*x^4*e^(2*x)*log(2) + 45*x^4*e^(x + 5)
*log(2) - 135*x^4*e^x*log(2) + 55*x^5*log(x) - 5*x^4*e^10*log(x) - 120*x^4*e^5*log(x) + 40*x^4*e^(2*x)*log(x)
+ 45*x^4*e^(x + 5)*log(x) - 135*x^4*e^x*log(x) - 10*x^5 + 30*x^4*e^15 + 365*x^4*e^10 + 280*x^4*e^5 - 65*x^4*e^
(2*x) - 5*x^4*e^(2*x + 10) - 90*x^4*e^(2*x + 5) - 5*x^4*e^(x + 15) - 75*x^4*e^(x + 10) + 210*x^4*e^(x + 5) + 1
88*x^4*e^x - 45*x^4*log(2) + 30*x^3*e^15*log(2) + 360*x^3*e^10*log(2) + 270*x^3*e^5*log(2) - 65*x^3*e^(2*x)*lo
g(2) - 5*x^3*e^(2*x + 10)*log(2) - 90*x^3*e^(2*x + 5)*log(2) - 5*x^3*e^(x + 15)*log(2) - 75*x^3*e^(x + 10)*log
(2) + 205*x^3*e^(x + 5)*log(2) + 195*x^3*e^x*log(2) - 45*x^4*log(x) + 30*x^3*e^15*log(x) + 360*x^3*e^10*log(x)
+ 270*x^3*e^5*log(x) - 65*x^3*e^(2*x)*log(x) - 5*x^3*e^(2*x + 10)*log(x) - 90*x^3*e^(2*x + 5)*log(x) - 5*x^3*
e^(x + 15)*log(x) - 75*x^3*e^(x + 10)*log(x) + 205*x^3*e^(x + 5)*log(x) + 195*x^3*e^x*log(x) + 45*x^4 + 29*x^3
*e^15 - 18*x^3*e^10 + 195*x^3*e^5 + 90*x^3*e^(2*x) + 10*x^3*e^(2*x + 10) + 60*x^3*e^(2*x + 5) + 10*x^3*e^(x +
15) + 89*x^3*e^(x + 10) - 288*x^3*e^(x + 5) - 283*x^3*e^x - 90*x^2*e^10*log(2) + 90*x^2*e^(2*x)*log(2) + 10*x^
2*e^(2*x + 10)*log(2) + 60*x^2*e^(2*x + 5)*log(2) + 10*x^2*e^(x + 15)*log(2) + 60*x^2*e^(x + 10)*log(2) - 180*
x^2*e^(x + 5)*log(2) - 270*x^2*e^x*log(2) - 90*x^2*e^10*log(x) + 90*x^2*e^(2*x)*log(x) + 10*x^2*e^(2*x + 10)*l
og(x) + 60*x^2*e^(2*x + 5)*log(x) + 10*x^2*e^(x + 15)*log(x) + 60*x^2*e^(x + 10)*log(x) - 180*x^2*e^(x + 5)*lo
g(x) - 270*x^2*e^x*log(x) + 45*x^2*e^20 + 303*x^2*e^15 + 321*x^2*e^10 + 297*x^2*e^5 - 15*x^2*e^(2*x + 15) - 90
*x^2*e^(2*x + 10) - 135*x^2*e^(2*x + 5) - 15*x^2*e^(x + 20) - 45*x^2*e^(x + 15) + 168*x^2*e^(x + 10) + 324*x^2
*e^(x + 5) + 18*x^2*e^x + 45*x*e^20*log(2) + 270*x*e^15*log(2) + 315*x*e^10*log(2) - 15*x*e^(2*x + 15)*log(2)
- 90*x*e^(2*x + 10)*log(2) - 135*x*e^(2*x + 5)*log(2) - 15*x*e^(x + 20)*log(2) - 45*x*e^(x + 15)*log(2) + 135*
x*e^(x + 10)*log(2) + 405*x*e^(x + 5)*log(2) + 45*x*e^20*log(x) + 270*x*e^15*log(x) + 315*x*e^10*log(x) - 15*x
*e^(2*x + 15)*log(x) - 90*x*e^(2*x + 10)*log(x) - 135*x*e^(2*x + 5)*log(x) - 15*x*e^(x + 20)*log(x) - 45*x*e^(
x + 15)*log(x) + 135*x*e^(x + 10)*log(x) + 405*x*e^(x + 5)*log(x) + 87*x*e^20 - 18*x*e^15 + 699*x*e^10 + 87*x*
e^(x + 15) - 288*x*e^(x + 10) - 27*x*e^(x + 5) + 45*e^20*log(2) + 405*e^10*log(2) + 45*e^(x + 15)*log(2) - 135
*e^(x + 10)*log(2) + 45*e^20*log(x) + 405*e^10*log(x) + 45*e^(x + 15)*log(x) - 135*e^(x + 10)*log(x) + 42*e^20
+ 378*e^10 + 42*e^(x + 15) - 126*e^(x + 10))/(4*x^6 - 8*x^5 + x^4*e^10 + 30*x^4*e^5 - 4*x^4*e^(2*x) - 4*x^4*e
^(x + 5) + 12*x^4*e^x + 13*x^4 - 2*x^3*e^10 - 36*x^3*e^5 + 8*x^3*e^(2*x) + 8*x^3*e^(x + 5) - 24*x^3*e^x - 18*x
^3 + 6*x^2*e^15 + 72*x^2*e^10 + 66*x^2*e^5 - 13*x^2*e^(2*x) - x^2*e^(2*x + 10) - 18*x^2*e^(2*x + 5) - x^2*e^(x
+ 15) - 15*x^2*e^(x + 10) + 41*x^2*e^(x + 5) + 39*x^2*e^x - 6*x*e^15 - 36*x*e^10 - 54*x*e^5 + 18*x*e^(2*x) +
2*x*e^(2*x + 10) + 12*x*e^(2*x + 5) + 2*x*e^(x + 15) + 6*x*e^(x + 10) - 18*x*e^(x + 5) - 54*x*e^x + 9*e^20 + 5
4*e^15 + 81*e^10 - 3*e^(2*x + 15) - 18*e^(2*x + 10) - 27*e^(2*x + 5) - 3*e^(x + 20) - 9*e^(x + 15) + 27*e^(x +
10) + 81*e^(x + 5))

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maple [B]  time = 0.07, size = 69, normalized size = 1.97

method	result	size
risch	\(5 x \ln \left (2 x \right )+\frac {x \left (5 x \,{\mathrm e}^{5+x}-5 x^{3}+5 x \,{\mathrm e}^{2 x}-15 x \,{\mathrm e}^{5}-15 \,{\mathrm e}^{x} x +{\mathrm e}^{5}+{\mathrm e}^{x}\right )}{{\mathrm e}^{5+x}+{\mathrm e}^{2 x}-x^{2}-3 \,{\mathrm e}^{5}-3 \,{\mathrm e}^{x}}\)	\(69\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((5*exp(x)^4+(10*exp(5)-30)*exp(x)^3+(5*exp(5)^2-60*exp(5)-10*x^2+45)*exp(x)^2+(-30*exp(5)^2+(-10*x^2+90)*
exp(5)+30*x^2)*exp(x)+45*exp(5)^2+30*x^2*exp(5)+5*x^4)*ln(2*x)+(10*x+5)*exp(x)^4+((20*x+10)*exp(5)-61*x-29)*ex
p(x)^3+((10*x+5)*exp(5)^2+(-122*x-58)*exp(5)-20*x^3-10*x^2+90*x+42)*exp(x)^2+((-61*x-29)*exp(5)^2+(-20*x^3-10*
x^2+180*x+84)*exp(5)+59*x^3+31*x^2)*exp(x)+(90*x+42)*exp(5)^2+(60*x^3+31*x^2)*exp(5)+10*x^5+5*x^4)/(exp(x)^4+(
2*exp(5)-6)*exp(x)^3+(exp(5)^2-12*exp(5)-2*x^2+9)*exp(x)^2+(-6*exp(5)^2+(-2*x^2+18)*exp(5)+6*x^2)*exp(x)+9*exp
(5)^2+6*x^2*exp(5)+x^4),x,method=_RETURNVERBOSE)

[Out]

5*x*ln(2*x)+x*(5*x*exp(5+x)-5*x^3+5*x*exp(2*x)-15*x*exp(5)-15*exp(x)*x+exp(5)+exp(x))/(exp(5+x)+exp(2*x)-x^2-3
*exp(5)-3*exp(x))

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maxima [B]  time = 0.58, size = 123, normalized size = 3.51 \begin {gather*} \frac {5 \, x^{4} + 5 \, x^{3} \log \relax (2) + 15 \, x^{2} e^{5} + x {\left (15 \, \log \relax (2) - 1\right )} e^{5} - 5 \, {\left (x^{2} + x \log \relax (2) + x \log \relax (x)\right )} e^{\left (2 \, x\right )} - {\left (5 \, x^{2} {\left (e^{5} - 3\right )} + 5 \, x {\left (e^{5} - 3\right )} \log \relax (x) + {\left (5 \, e^{5} \log \relax (2) - 15 \, \log \relax (2) + 1\right )} x\right )} e^{x} + 5 \, {\left (x^{3} + 3 \, x e^{5}\right )} \log \relax (x)}{x^{2} - {\left (e^{5} - 3\right )} e^{x} + 3 \, e^{5} - e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)^4+(10*exp(5)-30)*exp(x)^3+(5*exp(5)^2-60*exp(5)-10*x^2+45)*exp(x)^2+(-30*exp(5)^2+(-10*x^
2+90)*exp(5)+30*x^2)*exp(x)+45*exp(5)^2+30*x^2*exp(5)+5*x^4)*log(2*x)+(10*x+5)*exp(x)^4+((20*x+10)*exp(5)-61*x
-29)*exp(x)^3+((10*x+5)*exp(5)^2+(-122*x-58)*exp(5)-20*x^3-10*x^2+90*x+42)*exp(x)^2+((-61*x-29)*exp(5)^2+(-20*
x^3-10*x^2+180*x+84)*exp(5)+59*x^3+31*x^2)*exp(x)+(90*x+42)*exp(5)^2+(60*x^3+31*x^2)*exp(5)+10*x^5+5*x^4)/(exp
(x)^4+(2*exp(5)-6)*exp(x)^3+(exp(5)^2-12*exp(5)-2*x^2+9)*exp(x)^2+(-6*exp(5)^2+(-2*x^2+18)*exp(5)+6*x^2)*exp(x
)+9*exp(5)^2+6*x^2*exp(5)+x^4),x, algorithm="maxima")

[Out]

(5*x^4 + 5*x^3*log(2) + 15*x^2*e^5 + x*(15*log(2) - 1)*e^5 - 5*(x^2 + x*log(2) + x*log(x))*e^(2*x) - (5*x^2*(e
^5 - 3) + 5*x*(e^5 - 3)*log(x) + (5*e^5*log(2) - 15*log(2) + 1)*x)*e^x + 5*(x^3 + 3*x*e^5)*log(x))/(x^2 - (e^5
- 3)*e^x + 3*e^5 - e^(2*x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {{\mathrm {e}}^{2\,x}\,\left (90\,x-10\,x^2-20\,x^3+{\mathrm {e}}^{10}\,\left (10\,x+5\right )-{\mathrm {e}}^5\,\left (122\,x+58\right )+42\right )+{\mathrm {e}}^x\,\left ({\mathrm {e}}^5\,\left (-20\,x^3-10\,x^2+180\,x+84\right )+31\,x^2+59\,x^3-{\mathrm {e}}^{10}\,\left (61\,x+29\right )\right )+{\mathrm {e}}^5\,\left (60\,x^3+31\,x^2\right )+\ln \left (2\,x\right )\,\left (5\,{\mathrm {e}}^{4\,x}+45\,{\mathrm {e}}^{10}+30\,x^2\,{\mathrm {e}}^5-{\mathrm {e}}^{2\,x}\,\left (10\,x^2+60\,{\mathrm {e}}^5-5\,{\mathrm {e}}^{10}-45\right )+{\mathrm {e}}^{3\,x}\,\left (10\,{\mathrm {e}}^5-30\right )+5\,x^4-{\mathrm {e}}^x\,\left (30\,{\mathrm {e}}^{10}+{\mathrm {e}}^5\,\left (10\,x^2-90\right )-30\,x^2\right )\right )-{\mathrm {e}}^{3\,x}\,\left (61\,x-{\mathrm {e}}^5\,\left (20\,x+10\right )+29\right )+{\mathrm {e}}^{4\,x}\,\left (10\,x+5\right )+5\,x^4+10\,x^5+{\mathrm {e}}^{10}\,\left (90\,x+42\right )}{{\mathrm {e}}^{4\,x}+9\,{\mathrm {e}}^{10}+6\,x^2\,{\mathrm {e}}^5-{\mathrm {e}}^{2\,x}\,\left (2\,x^2+12\,{\mathrm {e}}^5-{\mathrm {e}}^{10}-9\right )+{\mathrm {e}}^{3\,x}\,\left (2\,{\mathrm {e}}^5-6\right )+x^4-{\mathrm {e}}^x\,\left (6\,{\mathrm {e}}^{10}+{\mathrm {e}}^5\,\left (2\,x^2-18\right )-6\,x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x)*(90*x - 10*x^2 - 20*x^3 + exp(10)*(10*x + 5) - exp(5)*(122*x + 58) + 42) + exp(x)*(exp(5)*(180*x
- 10*x^2 - 20*x^3 + 84) + 31*x^2 + 59*x^3 - exp(10)*(61*x + 29)) + exp(5)*(31*x^2 + 60*x^3) + log(2*x)*(5*exp
(4*x) + 45*exp(10) + 30*x^2*exp(5) - exp(2*x)*(60*exp(5) - 5*exp(10) + 10*x^2 - 45) + exp(3*x)*(10*exp(5) - 30
) + 5*x^4 - exp(x)*(30*exp(10) + exp(5)*(10*x^2 - 90) - 30*x^2)) - exp(3*x)*(61*x - exp(5)*(20*x + 10) + 29) +
exp(4*x)*(10*x + 5) + 5*x^4 + 10*x^5 + exp(10)*(90*x + 42))/(exp(4*x) + 9*exp(10) + 6*x^2*exp(5) - exp(2*x)*(
12*exp(5) - exp(10) + 2*x^2 - 9) + exp(3*x)*(2*exp(5) - 6) + x^4 - exp(x)*(6*exp(10) + exp(5)*(2*x^2 - 18) - 6
*x^2)),x)

[Out]

int((exp(2*x)*(90*x - 10*x^2 - 20*x^3 + exp(10)*(10*x + 5) - exp(5)*(122*x + 58) + 42) + exp(x)*(exp(5)*(180*x
- 10*x^2 - 20*x^3 + 84) + 31*x^2 + 59*x^3 - exp(10)*(61*x + 29)) + exp(5)*(31*x^2 + 60*x^3) + log(2*x)*(5*exp
(4*x) + 45*exp(10) + 30*x^2*exp(5) - exp(2*x)*(60*exp(5) - 5*exp(10) + 10*x^2 - 45) + exp(3*x)*(10*exp(5) - 30
) + 5*x^4 - exp(x)*(30*exp(10) + exp(5)*(10*x^2 - 90) - 30*x^2)) - exp(3*x)*(61*x - exp(5)*(20*x + 10) + 29) +
exp(4*x)*(10*x + 5) + 5*x^4 + 10*x^5 + exp(10)*(90*x + 42))/(exp(4*x) + 9*exp(10) + 6*x^2*exp(5) - exp(2*x)*(
12*exp(5) - exp(10) + 2*x^2 - 9) + exp(3*x)*(2*exp(5) - 6) + x^4 - exp(x)*(6*exp(10) + exp(5)*(2*x^2 - 18) - 6
*x^2)), x)

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sympy [A]  time = 0.56, size = 44, normalized size = 1.26 \begin {gather*} 5 x^{2} + 5 x \log {\left (2 x \right )} + \frac {x e^{x} + x e^{5}}{- x^{2} + e^{2 x} + \left (-3 + e^{5}\right ) e^{x} - 3 e^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((5*exp(x)**4+(10*exp(5)-30)*exp(x)**3+(5*exp(5)**2-60*exp(5)-10*x**2+45)*exp(x)**2+(-30*exp(5)**2+(
-10*x**2+90)*exp(5)+30*x**2)*exp(x)+45*exp(5)**2+30*x**2*exp(5)+5*x**4)*ln(2*x)+(10*x+5)*exp(x)**4+((20*x+10)*
exp(5)-61*x-29)*exp(x)**3+((10*x+5)*exp(5)**2+(-122*x-58)*exp(5)-20*x**3-10*x**2+90*x+42)*exp(x)**2+((-61*x-29
)*exp(5)**2+(-20*x**3-10*x**2+180*x+84)*exp(5)+59*x**3+31*x**2)*exp(x)+(90*x+42)*exp(5)**2+(60*x**3+31*x**2)*e
xp(5)+10*x**5+5*x**4)/(exp(x)**4+(2*exp(5)-6)*exp(x)**3+(exp(5)**2-12*exp(5)-2*x**2+9)*exp(x)**2+(-6*exp(5)**2
+(-2*x**2+18)*exp(5)+6*x**2)*exp(x)+9*exp(5)**2+6*x**2*exp(5)+x**4),x)

[Out]

5*x**2 + 5*x*log(2*x) + (x*exp(x) + x*exp(5))/(-x**2 + exp(2*x) + (-3 + exp(5))*exp(x) - 3*exp(5))

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