3.100.65 \(\int (36-24 e^5+18 x+(72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2) \log (4)+(72 x+32 e^{10} x+72 x^2+16 x^3+e^5 (-96 x-48 x^2)) \log ^2(4)+e^{2 x} (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} (2 x+2 x^2) \log ^2(4))+e^x (8 e^{10}+e^5 (-18-6 x)+(e^{10} (16+16 x)+e^5 (-24-44 x-10 x^2)) \log (4)+(e^{10} (16 x+8 x^2)+e^5 (-24 x-24 x^2-4 x^3)) \log ^2(4))) \, dx\)

Optimal. Leaf size=28 \[ \left (x+x \left (-e^5 \left (4+e^x\right )+2 (3+x)\right ) \left (\frac {1}{x}+\log (4)\right )\right )^2 \]

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Rubi [B]  time = 0.53, antiderivative size = 414, normalized size of antiderivative = 14.79, number of steps used = 41, number of rules used = 4, integrand size = 198, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6, 2196, 2194, 2176} \begin {gather*} 4 x^4 \log ^2(4)-4 e^{x+5} x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)+24 x^3 \log ^2(4)+12 x^3 \log (4)+9 x^2+12 e^{x+5} x^2 \log ^2(4)+e^{2 x+10} x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)-8 \left (3-e^5\right ) e^{x+5} x^2 \log ^2(4)-48 e^5 x^2 \log ^2(4)-10 e^{x+5} x^2 \log (4)+60 x^2 \log (4)+12 \left (3-2 e^5\right ) x+6 e^{x+5}+8 e^{x+10}+e^{2 x+10}-6 e^{x+5} (x+3)-24 e^{x+5} x \log ^2(4)+16 \left (3-e^5\right ) e^{x+5} x \log ^2(4)-8 \left (3-2 e^5\right ) e^{x+5} x \log ^2(4)+24 e^{x+5} \log ^2(4)-16 \left (3-e^5\right ) e^{x+5} \log ^2(4)+8 \left (3-2 e^5\right ) e^{x+5} \log ^2(4)+20 e^{x+5} x \log (4)+8 \left (9+4 e^{10}\right ) x \log (4)-4 \left (11-4 e^5\right ) e^{x+5} x \log (4)-20 e^{x+5} \log (4)-e^{2 x+10} \log (4)-\frac {8}{5} e^5 (5 x+6)^2 \log (4)+e^{2 x+10} (2 x+1) \log (4)-8 \left (3-2 e^5\right ) e^{x+5} \log (4)+4 \left (11-4 e^5\right ) e^{x+5} \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[36 - 24*E^5 + 18*x + (72 + 32*E^10 + E^5*(-96 - 80*x) + 120*x + 36*x^2)*Log[4] + (72*x + 32*E^10*x + 72*x^
2 + 16*x^3 + E^5*(-96*x - 48*x^2))*Log[4]^2 + E^(2*x)*(2*E^10 + E^10*(2 + 4*x)*Log[4] + E^10*(2*x + 2*x^2)*Log
[4]^2) + E^x*(8*E^10 + E^5*(-18 - 6*x) + (E^10*(16 + 16*x) + E^5*(-24 - 44*x - 10*x^2))*Log[4] + (E^10*(16*x +
8*x^2) + E^5*(-24*x - 24*x^2 - 4*x^3))*Log[4]^2),x]

[Out]

6*E^(5 + x) + 8*E^(10 + x) + E^(10 + 2*x) + 12*(3 - 2*E^5)*x + 9*x^2 - 6*E^(5 + x)*(3 + x) - 20*E^(5 + x)*Log[
4] - E^(10 + 2*x)*Log[4] + 4*E^(5 + x)*(11 - 4*E^5)*Log[4] - 8*E^(5 + x)*(3 - 2*E^5)*Log[4] + 20*E^(5 + x)*x*L
og[4] - 4*E^(5 + x)*(11 - 4*E^5)*x*Log[4] + 8*(9 + 4*E^10)*x*Log[4] + 60*x^2*Log[4] - 10*E^(5 + x)*x^2*Log[4]
+ 12*x^3*Log[4] + E^(10 + 2*x)*(1 + 2*x)*Log[4] - (8*E^5*(6 + 5*x)^2*Log[4])/5 + 24*E^(5 + x)*Log[4]^2 + 8*E^(
5 + x)*(3 - 2*E^5)*Log[4]^2 - 16*E^(5 + x)*(3 - E^5)*Log[4]^2 - 24*E^(5 + x)*x*Log[4]^2 - 8*E^(5 + x)*(3 - 2*E
^5)*x*Log[4]^2 + 16*E^(5 + x)*(3 - E^5)*x*Log[4]^2 - 48*E^5*x^2*Log[4]^2 + 12*E^(5 + x)*x^2*Log[4]^2 + E^(10 +
2*x)*x^2*Log[4]^2 - 8*E^(5 + x)*(3 - E^5)*x^2*Log[4]^2 + 4*(9 + 4*E^10)*x^2*Log[4]^2 + 24*x^3*Log[4]^2 - 16*E
^5*x^3*Log[4]^2 - 4*E^(5 + x)*x^3*Log[4]^2 + 4*x^4*Log[4]^2

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 2176

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[((c + d*x)^m
*(b*F^(g*(e + f*x)))^n)/(f*g*n*Log[F]), x] - Dist[(d*m)/(f*g*n*Log[F]), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !$UseGamma === True

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rule 2196

Int[(F_)^((c_.)*(v_))*(u_), x_Symbol] :> Int[ExpandIntegrand[F^(c*ExpandToSum[v, x]), u, x], x] /; FreeQ[{F, c
}, x] && PolynomialQ[u, x] && LinearQ[v, x] &&  !$UseGamma === True

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=12 \left (3-2 e^5\right ) x+9 x^2+\log (4) \int \left (72+32 e^{10}+e^5 (-96-80 x)+120 x+36 x^2\right ) \, dx+\log ^2(4) \int \left (72 x+32 e^{10} x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \, dx+\int e^{2 x} \left (2 e^{10}+e^{10} (2+4 x) \log (4)+e^{10} \left (2 x+2 x^2\right ) \log ^2(4)\right ) \, dx+\int e^x \left (8 e^{10}+e^5 (-18-6 x)+\left (e^{10} (16+16 x)+e^5 \left (-24-44 x-10 x^2\right )\right ) \log (4)+\left (e^{10} \left (16 x+8 x^2\right )+e^5 \left (-24 x-24 x^2-4 x^3\right )\right ) \log ^2(4)\right ) \, dx\\ &=12 \left (3-2 e^5\right ) x+9 x^2+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)+12 x^3 \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)+\log ^2(4) \int \left (\left (72+32 e^{10}\right ) x+72 x^2+16 x^3+e^5 \left (-96 x-48 x^2\right )\right ) \, dx+\int \left (2 e^{10+2 x}+2 e^{10+2 x} (1+2 x) \log (4)+2 e^{10+2 x} x (1+x) \log ^2(4)\right ) \, dx+\int \left (8 e^{10+x}-6 e^{5+x} (3+x)+2 e^{5+x} \left (-4 \left (3-2 e^5\right )-2 \left (11-4 e^5\right ) x-5 x^2\right ) \log (4)+4 e^{5+x} x \left (-2 \left (3-2 e^5\right )-2 \left (3-e^5\right ) x-x^2\right ) \log ^2(4)\right ) \, dx\\ &=12 \left (3-2 e^5\right ) x+9 x^2+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)+12 x^3 \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)+24 x^3 \log ^2(4)+4 x^4 \log ^2(4)+2 \int e^{10+2 x} \, dx-6 \int e^{5+x} (3+x) \, dx+8 \int e^{10+x} \, dx+(2 \log (4)) \int e^{10+2 x} (1+2 x) \, dx+(2 \log (4)) \int e^{5+x} \left (-4 \left (3-2 e^5\right )-2 \left (11-4 e^5\right ) x-5 x^2\right ) \, dx+\left (2 \log ^2(4)\right ) \int e^{10+2 x} x (1+x) \, dx+\left (4 \log ^2(4)\right ) \int e^{5+x} x \left (-2 \left (3-2 e^5\right )-2 \left (3-e^5\right ) x-x^2\right ) \, dx+\left (e^5 \log ^2(4)\right ) \int \left (-96 x-48 x^2\right ) \, dx\\ &=8 e^{10+x}+e^{10+2 x}+12 \left (3-2 e^5\right ) x+9 x^2-6 e^{5+x} (3+x)+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)+12 x^3 \log (4)+e^{10+2 x} (1+2 x) \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)-48 e^5 x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)+24 x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)+4 x^4 \log ^2(4)+6 \int e^{5+x} \, dx-(2 \log (4)) \int e^{10+2 x} \, dx+(2 \log (4)) \int \left (4 e^{5+x} \left (-3+2 e^5\right )+2 e^{5+x} \left (-11+4 e^5\right ) x-5 e^{5+x} x^2\right ) \, dx+\left (2 \log ^2(4)\right ) \int \left (e^{10+2 x} x+e^{10+2 x} x^2\right ) \, dx+\left (4 \log ^2(4)\right ) \int \left (2 e^{5+x} \left (-3+2 e^5\right ) x+2 e^{5+x} \left (-3+e^5\right ) x^2-e^{5+x} x^3\right ) \, dx\\ &=6 e^{5+x}+8 e^{10+x}+e^{10+2 x}+12 \left (3-2 e^5\right ) x+9 x^2-6 e^{5+x} (3+x)-e^{10+2 x} \log (4)+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)+12 x^3 \log (4)+e^{10+2 x} (1+2 x) \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)-48 e^5 x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)+24 x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)+4 x^4 \log ^2(4)-(10 \log (4)) \int e^{5+x} x^2 \, dx-\left (4 \left (11-4 e^5\right ) \log (4)\right ) \int e^{5+x} x \, dx-\left (8 \left (3-2 e^5\right ) \log (4)\right ) \int e^{5+x} \, dx+\left (2 \log ^2(4)\right ) \int e^{10+2 x} x \, dx+\left (2 \log ^2(4)\right ) \int e^{10+2 x} x^2 \, dx-\left (4 \log ^2(4)\right ) \int e^{5+x} x^3 \, dx-\left (8 \left (3-2 e^5\right ) \log ^2(4)\right ) \int e^{5+x} x \, dx-\left (8 \left (3-e^5\right ) \log ^2(4)\right ) \int e^{5+x} x^2 \, dx\\ &=6 e^{5+x}+8 e^{10+x}+e^{10+2 x}+12 \left (3-2 e^5\right ) x+9 x^2-6 e^{5+x} (3+x)-e^{10+2 x} \log (4)-8 e^{5+x} \left (3-2 e^5\right ) \log (4)-4 e^{5+x} \left (11-4 e^5\right ) x \log (4)+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)-10 e^{5+x} x^2 \log (4)+12 x^3 \log (4)+e^{10+2 x} (1+2 x) \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)+e^{10+2 x} x \log ^2(4)-8 e^{5+x} \left (3-2 e^5\right ) x \log ^2(4)-48 e^5 x^2 \log ^2(4)+e^{10+2 x} x^2 \log ^2(4)-8 e^{5+x} \left (3-e^5\right ) x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)+24 x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)-4 e^{5+x} x^3 \log ^2(4)+4 x^4 \log ^2(4)+(20 \log (4)) \int e^{5+x} x \, dx+\left (4 \left (11-4 e^5\right ) \log (4)\right ) \int e^{5+x} \, dx-\log ^2(4) \int e^{10+2 x} \, dx-\left (2 \log ^2(4)\right ) \int e^{10+2 x} x \, dx+\left (12 \log ^2(4)\right ) \int e^{5+x} x^2 \, dx+\left (8 \left (3-2 e^5\right ) \log ^2(4)\right ) \int e^{5+x} \, dx+\left (16 \left (3-e^5\right ) \log ^2(4)\right ) \int e^{5+x} x \, dx\\ &=6 e^{5+x}+8 e^{10+x}+e^{10+2 x}+12 \left (3-2 e^5\right ) x+9 x^2-6 e^{5+x} (3+x)-e^{10+2 x} \log (4)+4 e^{5+x} \left (11-4 e^5\right ) \log (4)-8 e^{5+x} \left (3-2 e^5\right ) \log (4)+20 e^{5+x} x \log (4)-4 e^{5+x} \left (11-4 e^5\right ) x \log (4)+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)-10 e^{5+x} x^2 \log (4)+12 x^3 \log (4)+e^{10+2 x} (1+2 x) \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)-\frac {1}{2} e^{10+2 x} \log ^2(4)+8 e^{5+x} \left (3-2 e^5\right ) \log ^2(4)-8 e^{5+x} \left (3-2 e^5\right ) x \log ^2(4)+16 e^{5+x} \left (3-e^5\right ) x \log ^2(4)-48 e^5 x^2 \log ^2(4)+12 e^{5+x} x^2 \log ^2(4)+e^{10+2 x} x^2 \log ^2(4)-8 e^{5+x} \left (3-e^5\right ) x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)+24 x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)-4 e^{5+x} x^3 \log ^2(4)+4 x^4 \log ^2(4)-(20 \log (4)) \int e^{5+x} \, dx+\log ^2(4) \int e^{10+2 x} \, dx-\left (24 \log ^2(4)\right ) \int e^{5+x} x \, dx-\left (16 \left (3-e^5\right ) \log ^2(4)\right ) \int e^{5+x} \, dx\\ &=6 e^{5+x}+8 e^{10+x}+e^{10+2 x}+12 \left (3-2 e^5\right ) x+9 x^2-6 e^{5+x} (3+x)-20 e^{5+x} \log (4)-e^{10+2 x} \log (4)+4 e^{5+x} \left (11-4 e^5\right ) \log (4)-8 e^{5+x} \left (3-2 e^5\right ) \log (4)+20 e^{5+x} x \log (4)-4 e^{5+x} \left (11-4 e^5\right ) x \log (4)+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)-10 e^{5+x} x^2 \log (4)+12 x^3 \log (4)+e^{10+2 x} (1+2 x) \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)+8 e^{5+x} \left (3-2 e^5\right ) \log ^2(4)-16 e^{5+x} \left (3-e^5\right ) \log ^2(4)-24 e^{5+x} x \log ^2(4)-8 e^{5+x} \left (3-2 e^5\right ) x \log ^2(4)+16 e^{5+x} \left (3-e^5\right ) x \log ^2(4)-48 e^5 x^2 \log ^2(4)+12 e^{5+x} x^2 \log ^2(4)+e^{10+2 x} x^2 \log ^2(4)-8 e^{5+x} \left (3-e^5\right ) x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)+24 x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)-4 e^{5+x} x^3 \log ^2(4)+4 x^4 \log ^2(4)+\left (24 \log ^2(4)\right ) \int e^{5+x} \, dx\\ &=6 e^{5+x}+8 e^{10+x}+e^{10+2 x}+12 \left (3-2 e^5\right ) x+9 x^2-6 e^{5+x} (3+x)-20 e^{5+x} \log (4)-e^{10+2 x} \log (4)+4 e^{5+x} \left (11-4 e^5\right ) \log (4)-8 e^{5+x} \left (3-2 e^5\right ) \log (4)+20 e^{5+x} x \log (4)-4 e^{5+x} \left (11-4 e^5\right ) x \log (4)+8 \left (9+4 e^{10}\right ) x \log (4)+60 x^2 \log (4)-10 e^{5+x} x^2 \log (4)+12 x^3 \log (4)+e^{10+2 x} (1+2 x) \log (4)-\frac {8}{5} e^5 (6+5 x)^2 \log (4)+24 e^{5+x} \log ^2(4)+8 e^{5+x} \left (3-2 e^5\right ) \log ^2(4)-16 e^{5+x} \left (3-e^5\right ) \log ^2(4)-24 e^{5+x} x \log ^2(4)-8 e^{5+x} \left (3-2 e^5\right ) x \log ^2(4)+16 e^{5+x} \left (3-e^5\right ) x \log ^2(4)-48 e^5 x^2 \log ^2(4)+12 e^{5+x} x^2 \log ^2(4)+e^{10+2 x} x^2 \log ^2(4)-8 e^{5+x} \left (3-e^5\right ) x^2 \log ^2(4)+4 \left (9+4 e^{10}\right ) x^2 \log ^2(4)+24 x^3 \log ^2(4)-16 e^5 x^3 \log ^2(4)-4 e^{5+x} x^3 \log ^2(4)+4 x^4 \log ^2(4)\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.60, size = 156, normalized size = 5.57 \begin {gather*} e^{2 (5+x)} (1+x \log (4))^2+8 e^{10+x} (1+x \log (4))^2+16 e^{10} x \log (4) (2+x \log (4))-8 e^5 x \left (3+12 \log (4)+2 x^2 \log ^2(4)+x \log (4) (5+6 \log (4))\right )+x \left (36+72 \log (4)+4 x^3 \log ^2(4)+x \left (9+60 \log (4)+36 \log ^2(4)\right )+12 x^2 \log (4) (1+\log (16))\right )-2 e^{5+x} \left (6+2 x^3 \log ^2(4)+x^2 \log (4) (5+6 \log (4))+3 x (1+\log (256))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[36 - 24*E^5 + 18*x + (72 + 32*E^10 + E^5*(-96 - 80*x) + 120*x + 36*x^2)*Log[4] + (72*x + 32*E^10*x +
72*x^2 + 16*x^3 + E^5*(-96*x - 48*x^2))*Log[4]^2 + E^(2*x)*(2*E^10 + E^10*(2 + 4*x)*Log[4] + E^10*(2*x + 2*x^
2)*Log[4]^2) + E^x*(8*E^10 + E^5*(-18 - 6*x) + (E^10*(16 + 16*x) + E^5*(-24 - 44*x - 10*x^2))*Log[4] + (E^10*(
16*x + 8*x^2) + E^5*(-24*x - 24*x^2 - 4*x^3))*Log[4]^2),x]

[Out]

E^(2*(5 + x))*(1 + x*Log[4])^2 + 8*E^(10 + x)*(1 + x*Log[4])^2 + 16*E^10*x*Log[4]*(2 + x*Log[4]) - 8*E^5*x*(3
+ 12*Log[4] + 2*x^2*Log[4]^2 + x*Log[4]*(5 + 6*Log[4])) + x*(36 + 72*Log[4] + 4*x^3*Log[4]^2 + x*(9 + 60*Log[4
] + 36*Log[4]^2) + 12*x^2*Log[4]*(1 + Log[16])) - 2*E^(5 + x)*(6 + 2*x^3*Log[4]^2 + x^2*Log[4]*(5 + 6*Log[4])
+ 3*x*(1 + Log[256]))

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fricas [B]  time = 0.96, size = 182, normalized size = 6.50 \begin {gather*} 16 \, {\left (x^{4} + 6 \, x^{3} + 4 \, x^{2} e^{10} + 9 \, x^{2} - 4 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \relax (2)^{2} + 9 \, x^{2} - 24 \, x e^{5} + {\left (4 \, x^{2} e^{10} \log \relax (2)^{2} + 4 \, x e^{10} \log \relax (2) + e^{10}\right )} e^{\left (2 \, x\right )} + 2 \, {\left (8 \, {\left (2 \, x^{2} e^{10} - {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \relax (2)^{2} - 3 \, {\left (x + 2\right )} e^{5} + 2 \, {\left (8 \, x e^{10} - {\left (5 \, x^{2} + 12 \, x\right )} e^{5}\right )} \log \relax (2) + 4 \, e^{10}\right )} e^{x} + 8 \, {\left (3 \, x^{3} + 15 \, x^{2} + 8 \, x e^{10} - 2 \, {\left (5 \, x^{2} + 12 \, x\right )} e^{5} + 18 \, x\right )} \log \relax (2) + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*(2*x^2+2*x)*exp(5)^2*log(2)^2+2*(4*x+2)*exp(5)^2*log(2)+2*exp(5)^2)*exp(x)^2+(4*((8*x^2+16*x)*exp
(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*log(2)^2+2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*log(2)+8*exp(5)^2+
(-6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^2+72*x)*log(2)^2+2*(32*exp(5)^2+(-
80*x-96)*exp(5)+36*x^2+120*x+72)*log(2)-24*exp(5)+18*x+36,x, algorithm="fricas")

[Out]

16*(x^4 + 6*x^3 + 4*x^2*e^10 + 9*x^2 - 4*(x^3 + 3*x^2)*e^5)*log(2)^2 + 9*x^2 - 24*x*e^5 + (4*x^2*e^10*log(2)^2
+ 4*x*e^10*log(2) + e^10)*e^(2*x) + 2*(8*(2*x^2*e^10 - (x^3 + 3*x^2)*e^5)*log(2)^2 - 3*(x + 2)*e^5 + 2*(8*x*e
^10 - (5*x^2 + 12*x)*e^5)*log(2) + 4*e^10)*e^x + 8*(3*x^3 + 15*x^2 + 8*x*e^10 - 2*(5*x^2 + 12*x)*e^5 + 18*x)*l
og(2) + 36*x

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giac [B]  time = 0.14, size = 176, normalized size = 6.29 \begin {gather*} 16 \, {\left (x^{4} + 6 \, x^{3} + 4 \, x^{2} e^{10} + 9 \, x^{2} - 4 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \relax (2)^{2} + 9 \, x^{2} - 24 \, x e^{5} + {\left (4 \, x^{2} \log \relax (2)^{2} + 4 \, x \log \relax (2) + 1\right )} e^{\left (2 \, x + 10\right )} + 8 \, {\left (4 \, x^{2} \log \relax (2)^{2} + 4 \, x \log \relax (2) + 1\right )} e^{\left (x + 10\right )} - 2 \, {\left (8 \, x^{3} \log \relax (2)^{2} + 24 \, x^{2} \log \relax (2)^{2} + 10 \, x^{2} \log \relax (2) + 24 \, x \log \relax (2) + 3 \, x + 6\right )} e^{\left (x + 5\right )} + 8 \, {\left (3 \, x^{3} + 15 \, x^{2} + 8 \, x e^{10} - 2 \, {\left (5 \, x^{2} + 12 \, x\right )} e^{5} + 18 \, x\right )} \log \relax (2) + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*(2*x^2+2*x)*exp(5)^2*log(2)^2+2*(4*x+2)*exp(5)^2*log(2)+2*exp(5)^2)*exp(x)^2+(4*((8*x^2+16*x)*exp
(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*log(2)^2+2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*log(2)+8*exp(5)^2+
(-6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^2+72*x)*log(2)^2+2*(32*exp(5)^2+(-
80*x-96)*exp(5)+36*x^2+120*x+72)*log(2)-24*exp(5)+18*x+36,x, algorithm="giac")

[Out]

16*(x^4 + 6*x^3 + 4*x^2*e^10 + 9*x^2 - 4*(x^3 + 3*x^2)*e^5)*log(2)^2 + 9*x^2 - 24*x*e^5 + (4*x^2*log(2)^2 + 4*
x*log(2) + 1)*e^(2*x + 10) + 8*(4*x^2*log(2)^2 + 4*x*log(2) + 1)*e^(x + 10) - 2*(8*x^3*log(2)^2 + 24*x^2*log(2
)^2 + 10*x^2*log(2) + 24*x*log(2) + 3*x + 6)*e^(x + 5) + 8*(3*x^3 + 15*x^2 + 8*x*e^10 - 2*(5*x^2 + 12*x)*e^5 +
18*x)*log(2) + 36*x

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maple [B]  time = 0.07, size = 216, normalized size = 7.71

method	result	size
risch	\(\left (4 \,{\mathrm e}^{10} \ln \relax (2)^{2} x^{2}+4 x \,{\mathrm e}^{10} \ln \relax (2)+{\mathrm e}^{10}\right ) {\mathrm e}^{2 x}+\left (32 \,{\mathrm e}^{10} \ln \relax (2)^{2} x^{2}-16 \ln \relax (2)^{2} x^{3} {\mathrm e}^{5}-48 x^{2} {\mathrm e}^{5} \ln \relax (2)^{2}+32 x \,{\mathrm e}^{10} \ln \relax (2)-20 x^{2} {\mathrm e}^{5} \ln \relax (2)-48 x \,{\mathrm e}^{5} \ln \relax (2)+8 \,{\mathrm e}^{10}-6 x \,{\mathrm e}^{5}-12 \,{\mathrm e}^{5}\right ) {\mathrm e}^{x}+16 x^{4} \ln \relax (2)^{2}-64 \ln \relax (2)^{2} x^{3} {\mathrm e}^{5}+96 x^{3} \ln \relax (2)^{2}-192 x^{2} {\mathrm e}^{5} \ln \relax (2)^{2}+64 \,{\mathrm e}^{10} \ln \relax (2)^{2} x^{2}+144 x^{2} \ln \relax (2)^{2}+64 x \,{\mathrm e}^{10} \ln \relax (2)-80 x^{2} {\mathrm e}^{5} \ln \relax (2)+24 x^{3} \ln \relax (2)-192 x \,{\mathrm e}^{5} \ln \relax (2)+120 x^{2} \ln \relax (2)+144 x \ln \relax (2)-24 x \,{\mathrm e}^{5}+9 x^{2}+36 x\)	\(216\)
norman	\(\left (-12 \,{\mathrm e}^{5}+8 \,{\mathrm e}^{10}\right ) {\mathrm e}^{x}+\left (-64 \,{\mathrm e}^{5} \ln \relax (2)^{2}+96 \ln \relax (2)^{2}+24 \ln \relax (2)\right ) x^{3}+\left (36-192 \,{\mathrm e}^{5} \ln \relax (2)+144 \ln \relax (2)-24 \,{\mathrm e}^{5}+64 \,{\mathrm e}^{10} \ln \relax (2)\right ) x +\left (64 \,{\mathrm e}^{10} \ln \relax (2)^{2}-192 \,{\mathrm e}^{5} \ln \relax (2)^{2}-80 \,{\mathrm e}^{5} \ln \relax (2)+144 \ln \relax (2)^{2}+120 \ln \relax (2)+9\right ) x^{2}+{\mathrm e}^{10} {\mathrm e}^{2 x}+\left (-48 \,{\mathrm e}^{5} \ln \relax (2)+32 \,{\mathrm e}^{10} \ln \relax (2)-6 \,{\mathrm e}^{5}\right ) x \,{\mathrm e}^{x}+\left (-48 \,{\mathrm e}^{5} \ln \relax (2)^{2}-20 \,{\mathrm e}^{5} \ln \relax (2)+32 \,{\mathrm e}^{10} \ln \relax (2)^{2}\right ) x^{2} {\mathrm e}^{x}+16 x^{4} \ln \relax (2)^{2}-16 \,{\mathrm e}^{5} {\mathrm e}^{x} \ln \relax (2)^{2} x^{3}+4 \,{\mathrm e}^{10} {\mathrm e}^{2 x} \ln \relax (2) x +4 \,{\mathrm e}^{10} {\mathrm e}^{2 x} \ln \relax (2)^{2} x^{2}\)	\(220\)
default	\(-6 x \,{\mathrm e}^{5} {\mathrm e}^{x}+36 x -192 x \,{\mathrm e}^{5} \ln \relax (2)-80 x^{2} {\mathrm e}^{5} \ln \relax (2)-24 x \,{\mathrm e}^{5}+9 x^{2}+16 x^{4} \ln \relax (2)^{2}+96 x^{3} \ln \relax (2)^{2}+144 x^{2} \ln \relax (2)^{2}+144 x \ln \relax (2)+120 x^{2} \ln \relax (2)+24 x^{3} \ln \relax (2)-12 \,{\mathrm e}^{5} {\mathrm e}^{x}-192 x^{2} {\mathrm e}^{5} \ln \relax (2)^{2}+32 \,{\mathrm e}^{10} {\mathrm e}^{x} \ln \relax (2)^{2} x^{2}+32 \,{\mathrm e}^{10} {\mathrm e}^{x} \ln \relax (2) x +4 \,{\mathrm e}^{10} {\mathrm e}^{2 x} \ln \relax (2) x +4 \,{\mathrm e}^{10} {\mathrm e}^{2 x} \ln \relax (2)^{2} x^{2}-16 \,{\mathrm e}^{5} {\mathrm e}^{x} \ln \relax (2)^{2} x^{3}-48 \,{\mathrm e}^{5} {\mathrm e}^{x} \ln \relax (2)^{2} x^{2}-20 \,{\mathrm e}^{5} {\mathrm e}^{x} \ln \relax (2) x^{2}-48 \,{\mathrm e}^{5} {\mathrm e}^{x} \ln \relax (2) x -64 \ln \relax (2)^{2} x^{3} {\mathrm e}^{5}+64 \,{\mathrm e}^{10} \ln \relax (2)^{2} x^{2}+64 x \,{\mathrm e}^{10} \ln \relax (2)+{\mathrm e}^{10} {\mathrm e}^{2 x}+8 \,{\mathrm e}^{10} {\mathrm e}^{x}\)	\(253\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*(2*x^2+2*x)*exp(5)^2*ln(2)^2+2*(4*x+2)*exp(5)^2*ln(2)+2*exp(5)^2)*exp(x)^2+(4*((8*x^2+16*x)*exp(5)^2+(-
4*x^3-24*x^2-24*x)*exp(5))*ln(2)^2+2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*ln(2)+8*exp(5)^2+(-6*x-18)*
exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^2+72*x)*ln(2)^2+2*(32*exp(5)^2+(-80*x-96)*ex
p(5)+36*x^2+120*x+72)*ln(2)-24*exp(5)+18*x+36,x,method=_RETURNVERBOSE)

[Out]

(4*exp(10)*ln(2)^2*x^2+4*x*exp(10)*ln(2)+exp(10))*exp(2*x)+(32*exp(10)*ln(2)^2*x^2-16*ln(2)^2*x^3*exp(5)-48*x^
2*exp(5)*ln(2)^2+32*x*exp(10)*ln(2)-20*x^2*exp(5)*ln(2)-48*x*exp(5)*ln(2)+8*exp(10)-6*x*exp(5)-12*exp(5))*exp(
x)+16*x^4*ln(2)^2-64*ln(2)^2*x^3*exp(5)+96*x^3*ln(2)^2-192*x^2*exp(5)*ln(2)^2+64*exp(10)*ln(2)^2*x^2+144*x^2*l
n(2)^2+64*x*exp(10)*ln(2)-80*x^2*exp(5)*ln(2)+24*x^3*ln(2)-192*x*exp(5)*ln(2)+120*x^2*ln(2)+144*x*ln(2)-24*x*e
xp(5)+9*x^2+36*x

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maxima [B]  time = 0.44, size = 188, normalized size = 6.71 \begin {gather*} 16 \, {\left (x^{4} + 6 \, x^{3} + 4 \, x^{2} e^{10} + 9 \, x^{2} - 4 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \relax (2)^{2} + 9 \, x^{2} - 24 \, x e^{5} + {\left (4 \, x^{2} e^{10} \log \relax (2)^{2} + 4 \, x e^{10} \log \relax (2) + e^{10}\right )} e^{\left (2 \, x\right )} - 2 \, {\left (8 \, x^{3} e^{5} \log \relax (2)^{2} - 2 \, {\left (8 \, e^{10} \log \relax (2)^{2} - {\left (12 \, \log \relax (2)^{2} + 5 \, \log \relax (2)\right )} e^{5}\right )} x^{2} + {\left (3 \, {\left (8 \, \log \relax (2) + 1\right )} e^{5} - 16 \, e^{10} \log \relax (2)\right )} x - 4 \, e^{10} + 6 \, e^{5}\right )} e^{x} + 8 \, {\left (3 \, x^{3} + 15 \, x^{2} + 8 \, x e^{10} - 2 \, {\left (5 \, x^{2} + 12 \, x\right )} e^{5} + 18 \, x\right )} \log \relax (2) + 36 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*(2*x^2+2*x)*exp(5)^2*log(2)^2+2*(4*x+2)*exp(5)^2*log(2)+2*exp(5)^2)*exp(x)^2+(4*((8*x^2+16*x)*exp
(5)^2+(-4*x^3-24*x^2-24*x)*exp(5))*log(2)^2+2*((16*x+16)*exp(5)^2+(-10*x^2-44*x-24)*exp(5))*log(2)+8*exp(5)^2+
(-6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)^2+(-48*x^2-96*x)*exp(5)+16*x^3+72*x^2+72*x)*log(2)^2+2*(32*exp(5)^2+(-
80*x-96)*exp(5)+36*x^2+120*x+72)*log(2)-24*exp(5)+18*x+36,x, algorithm="maxima")

[Out]

16*(x^4 + 6*x^3 + 4*x^2*e^10 + 9*x^2 - 4*(x^3 + 3*x^2)*e^5)*log(2)^2 + 9*x^2 - 24*x*e^5 + (4*x^2*e^10*log(2)^2
+ 4*x*e^10*log(2) + e^10)*e^(2*x) - 2*(8*x^3*e^5*log(2)^2 - 2*(8*e^10*log(2)^2 - (12*log(2)^2 + 5*log(2))*e^5
)*x^2 + (3*(8*log(2) + 1)*e^5 - 16*e^10*log(2))*x - 4*e^10 + 6*e^5)*e^x + 8*(3*x^3 + 15*x^2 + 8*x*e^10 - 2*(5*
x^2 + 12*x)*e^5 + 18*x)*log(2) + 36*x

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mupad [B]  time = 0.38, size = 189, normalized size = 6.75 \begin {gather*} {\mathrm {e}}^{2\,x+10}+16\,x^4\,{\ln \relax (2)}^2+x\,\left (144\,\ln \relax (2)-24\,{\mathrm {e}}^5-192\,{\mathrm {e}}^5\,\ln \relax (2)+64\,{\mathrm {e}}^{10}\,\ln \relax (2)+36\right )+{\mathrm {e}}^{x+5}\,\left (8\,{\mathrm {e}}^5-12\right )+x^2\,\left (120\,\ln \relax (2)-80\,{\mathrm {e}}^5\,\ln \relax (2)-192\,{\mathrm {e}}^5\,{\ln \relax (2)}^2+64\,{\mathrm {e}}^{10}\,{\ln \relax (2)}^2+144\,{\ln \relax (2)}^2+9\right )-16\,x^3\,{\mathrm {e}}^{x+5}\,{\ln \relax (2)}^2-2\,x\,{\mathrm {e}}^{x+5}\,\left (24\,\ln \relax (2)-16\,{\mathrm {e}}^5\,\ln \relax (2)+3\right )+4\,x^2\,{\mathrm {e}}^{2\,x+10}\,{\ln \relax (2)}^2+4\,x\,{\mathrm {e}}^{2\,x+10}\,\ln \relax (2)+8\,x^3\,\ln \relax (2)\,\left (12\,\ln \relax (2)-8\,{\mathrm {e}}^5\,\ln \relax (2)+3\right )-4\,x^2\,{\mathrm {e}}^{x+5}\,\ln \relax (2)\,\left (12\,\ln \relax (2)-8\,{\mathrm {e}}^5\,\ln \relax (2)+5\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(18*x - 24*exp(5) + exp(2*x)*(2*exp(10) + 2*exp(10)*log(2)*(4*x + 2) + 4*exp(10)*log(2)^2*(2*x + 2*x^2)) +
4*log(2)^2*(72*x - exp(5)*(96*x + 48*x^2) + 32*x*exp(10) + 72*x^2 + 16*x^3) + exp(x)*(8*exp(10) + 4*log(2)^2*(
exp(10)*(16*x + 8*x^2) - exp(5)*(24*x + 24*x^2 + 4*x^3)) - 2*log(2)*(exp(5)*(44*x + 10*x^2 + 24) - exp(10)*(16
*x + 16)) - exp(5)*(6*x + 18)) + 2*log(2)*(120*x + 32*exp(10) + 36*x^2 - exp(5)*(80*x + 96) + 72) + 36,x)

[Out]

exp(2*x + 10) + 16*x^4*log(2)^2 + x*(144*log(2) - 24*exp(5) - 192*exp(5)*log(2) + 64*exp(10)*log(2) + 36) + ex
p(x + 5)*(8*exp(5) - 12) + x^2*(120*log(2) - 80*exp(5)*log(2) - 192*exp(5)*log(2)^2 + 64*exp(10)*log(2)^2 + 14
4*log(2)^2 + 9) - 16*x^3*exp(x + 5)*log(2)^2 - 2*x*exp(x + 5)*(24*log(2) - 16*exp(5)*log(2) + 3) + 4*x^2*exp(2
*x + 10)*log(2)^2 + 4*x*exp(2*x + 10)*log(2) + 8*x^3*log(2)*(12*log(2) - 8*exp(5)*log(2) + 3) - 4*x^2*exp(x +
5)*log(2)*(12*log(2) - 8*exp(5)*log(2) + 5)

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sympy [B]  time = 0.32, size = 236, normalized size = 8.43 \begin {gather*} 16 x^{4} \log {\relax (2 )}^{2} + x^{3} \left (- 64 e^{5} \log {\relax (2 )}^{2} + 24 \log {\relax (2 )} + 96 \log {\relax (2 )}^{2}\right ) + x^{2} \left (- 192 e^{5} \log {\relax (2 )}^{2} - 80 e^{5} \log {\relax (2 )} + 9 + 144 \log {\relax (2 )}^{2} + 120 \log {\relax (2 )} + 64 e^{10} \log {\relax (2 )}^{2}\right ) + x \left (- 192 e^{5} \log {\relax (2 )} - 24 e^{5} + 36 + 144 \log {\relax (2 )} + 64 e^{10} \log {\relax (2 )}\right ) + \left (4 x^{2} e^{10} \log {\relax (2 )}^{2} + 4 x e^{10} \log {\relax (2 )} + e^{10}\right ) e^{2 x} + \left (- 16 x^{3} e^{5} \log {\relax (2 )}^{2} - 48 x^{2} e^{5} \log {\relax (2 )}^{2} - 20 x^{2} e^{5} \log {\relax (2 )} + 32 x^{2} e^{10} \log {\relax (2 )}^{2} - 48 x e^{5} \log {\relax (2 )} - 6 x e^{5} + 32 x e^{10} \log {\relax (2 )} - 12 e^{5} + 8 e^{10}\right ) e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*(2*x**2+2*x)*exp(5)**2*ln(2)**2+2*(4*x+2)*exp(5)**2*ln(2)+2*exp(5)**2)*exp(x)**2+(4*((8*x**2+16*x
)*exp(5)**2+(-4*x**3-24*x**2-24*x)*exp(5))*ln(2)**2+2*((16*x+16)*exp(5)**2+(-10*x**2-44*x-24)*exp(5))*ln(2)+8*
exp(5)**2+(-6*x-18)*exp(5))*exp(x)+4*(32*x*exp(5)**2+(-48*x**2-96*x)*exp(5)+16*x**3+72*x**2+72*x)*ln(2)**2+2*(
32*exp(5)**2+(-80*x-96)*exp(5)+36*x**2+120*x+72)*ln(2)-24*exp(5)+18*x+36,x)

[Out]

16*x**4*log(2)**2 + x**3*(-64*exp(5)*log(2)**2 + 24*log(2) + 96*log(2)**2) + x**2*(-192*exp(5)*log(2)**2 - 80*
exp(5)*log(2) + 9 + 144*log(2)**2 + 120*log(2) + 64*exp(10)*log(2)**2) + x*(-192*exp(5)*log(2) - 24*exp(5) + 3
6 + 144*log(2) + 64*exp(10)*log(2)) + (4*x**2*exp(10)*log(2)**2 + 4*x*exp(10)*log(2) + exp(10))*exp(2*x) + (-1
6*x**3*exp(5)*log(2)**2 - 48*x**2*exp(5)*log(2)**2 - 20*x**2*exp(5)*log(2) + 32*x**2*exp(10)*log(2)**2 - 48*x*
exp(5)*log(2) - 6*x*exp(5) + 32*x*exp(10)*log(2) - 12*exp(5) + 8*exp(10))*exp(x)

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