∫ 30−20e4+e2x(10−40e4)+10x+e3x(10−40e4−x3)+ex(30−20e4+10x−3x3−x4)+(6e4+3xx2+e4+x(18x2+6x3)) log(3+e2x+x)+(−12e8+3xx+e8+x(−36x−12x2)) log2(3+e2x+x)+(8e12+3x+e12+x(24+8x)) log3(3+e2x+x)______________ −3x3−e2xx3−e3xx3−x4+ex(−3x3−x4)+(6e4+2xx2+6e4+3xx2+e4(18x2+6x3)+e4+x(18x2+6x3)) log(3+e2x+x)+(−12e8+2xx−12e8+3xx+e8(−36x−12x2)+e8+x(−36x−12x2)) log2(3+e2x+x)+(8e12+2x+8e12+3x+e12(24+8x)+e12+x(24+8x)) log3(3+e2x+x) dx

3.38.2 \(\int \frac {30-20 e^4+e^{2 x} (10-40 e^4)+10 x+e^{3 x} (10-40 e^4-x^3)+e^x (30-20 e^4+10 x-3 x^3-x^4)+(6 e^{4+3 x} x^2+e^{4+x} (18 x^2+6 x^3)) \log (3+e^{2 x}+x)+(-12 e^{8+3 x} x+e^{8+x} (-36 x-12 x^2)) \log ^2(3+e^{2 x}+x)+(8 e^{12+3 x}+e^{12+x} (24+8 x)) \log ^3(3+e^{2 x}+x)}{-3 x^3-e^{2 x} x^3-e^{3 x} x^3-x^4+e^x (-3 x^3-x^4)+(6 e^{4+2 x} x^2+6 e^{4+3 x} x^2+e^4 (18 x^2+6 x^3)+e^{4+x} (18 x^2+6 x^3)) \log (3+e^{2 x}+x)+(-12 e^{8+2 x} x-12 e^{8+3 x} x+e^8 (-36 x-12 x^2)+e^{8+x} (-36 x-12 x^2)) \log ^2(3+e^{2 x}+x)+(8 e^{12+2 x}+8 e^{12+3 x}+e^{12} (24+8 x)+e^{12+x} (24+8 x)) \log ^3(3+e^{2 x}+x)} \, dx\)

Optimal. Leaf size=29 \[ \log \left (1+e^x\right )+\frac {5}{\left (-x+2 e^4 \log \left (3+e^{2 x}+x\right )\right )^2} \]

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Rubi [F] time = 4.07, 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 {30-20 e^4+e^{2 x} \left (10-40 e^4\right )+10 x+e^{3 x} \left (10-40 e^4-x^3\right )+e^x \left (30-20 e^4+10 x-3 x^3-x^4\right )+\left (6 e^{4+3 x} x^2+e^{4+x} \left (18 x^2+6 x^3\right )\right ) \log \left (3+e^{2 x}+x\right )+\left (-12 e^{8+3 x} x+e^{8+x} \left (-36 x-12 x^2\right )\right ) \log ^2\left (3+e^{2 x}+x\right )+\left (8 e^{12+3 x}+e^{12+x} (24+8 x)\right ) \log ^3\left (3+e^{2 x}+x\right )}{-3 x^3-e^{2 x} x^3-e^{3 x} x^3-x^4+e^x \left (-3 x^3-x^4\right )+\left (6 e^{4+2 x} x^2+6 e^{4+3 x} x^2+e^4 \left (18 x^2+6 x^3\right )+e^{4+x} \left (18 x^2+6 x^3\right )\right ) \log \left (3+e^{2 x}+x\right )+\left (-12 e^{8+2 x} x-12 e^{8+3 x} x+e^8 \left (-36 x-12 x^2\right )+e^{8+x} \left (-36 x-12 x^2\right )\right ) \log ^2\left (3+e^{2 x}+x\right )+\left (8 e^{12+2 x}+8 e^{12+3 x}+e^{12} (24+8 x)+e^{12+x} (24+8 x)\right ) \log ^3\left (3+e^{2 x}+x\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(30 - 20*E^4 + E^(2*x)*(10 - 40*E^4) + 10*x + E^(3*x)*(10 - 40*E^4 - x^3) + E^x*(30 - 20*E^4 + 10*x - 3*x^

3 - x^4) + (6*E^(4 + 3*x)*x^2 + E^(4 + x)*(18*x^2 + 6*x^3))*Log[3 + E^(2*x) + x] + (-12*E^(8 + 3*x)*x + E^(8 +

x)*(-36*x - 12*x^2))*Log[3 + E^(2*x) + x]^2 + (8*E^(12 + 3*x) + E^(12 + x)*(24 + 8*x))*Log[3 + E^(2*x) + x]^3

)/(-3*x^3 - E^(2*x)*x^3 - E^(3*x)*x^3 - x^4 + E^x*(-3*x^3 - x^4) + (6*E^(4 + 2*x)*x^2 + 6*E^(4 + 3*x)*x^2 + E^

4*(18*x^2 + 6*x^3) + E^(4 + x)*(18*x^2 + 6*x^3))*Log[3 + E^(2*x) + x] + (-12*E^(8 + 2*x)*x - 12*E^(8 + 3*x)*x

+ E^8*(-36*x - 12*x^2) + E^(8 + x)*(-36*x - 12*x^2))*Log[3 + E^(2*x) + x]^2 + (8*E^(12 + 2*x) + 8*E^(12 + 3*x)

+ E^12*(24 + 8*x) + E^(12 + x)*(24 + 8*x))*Log[3 + E^(2*x) + x]^3),x]

[Out]

Log[1 + E^x] - 10*(1 - 4*E^4)*Defer[Int][(x - 2*E^4*Log[3 + E^(2*x) + x])^(-3), x] - 100*E^4*Defer[Int][1/((3

+ E^(2*x) + x)*(x - 2*E^4*Log[3 + E^(2*x) + x])^3), x] - 40*E^4*Defer[Int][x/((3 + E^(2*x) + x)*(x - 2*E^4*Log

[3 + E^(2*x) + x])^3), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {20 e^4+20 e^{4+x}+40 e^{4+3 x}-10 e^{2 x} \left (1-4 e^4\right )-10 (3+x)+e^{3 x} \left (-10+x^3\right )+e^x \left (-30-10 x+3 x^3+x^4\right )-6 e^{4+x} x^2 \left (3+e^{2 x}+x\right ) \log \left (3+e^{2 x}+x\right )+12 e^{8+x} x \left (3+e^{2 x}+x\right ) \log ^2\left (3+e^{2 x}+x\right )-8 e^{12+x} \left (3+e^{2 x}+x\right ) \log ^3\left (3+e^{2 x}+x\right )}{\left (1+e^x\right ) \left (3+e^{2 x}+x\right ) \left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx\\ &=\int \left (-\frac {1}{1+e^x}+\frac {20 e^4 (5+2 x)}{\left (3+e^{2 x}+x\right ) \left (-x+2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3}+\frac {-10 \left (1-4 e^4\right )+x^3-6 e^4 x^2 \log \left (3+e^{2 x}+x\right )+12 e^8 x \log ^2\left (3+e^{2 x}+x\right )-8 e^{12} \log ^3\left (3+e^{2 x}+x\right )}{\left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3}\right ) \, dx\\ &=\left (20 e^4\right ) \int \frac {5+2 x}{\left (3+e^{2 x}+x\right ) \left (-x+2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx-\int \frac {1}{1+e^x} \, dx+\int \frac {-10 \left (1-4 e^4\right )+x^3-6 e^4 x^2 \log \left (3+e^{2 x}+x\right )+12 e^8 x \log ^2\left (3+e^{2 x}+x\right )-8 e^{12} \log ^3\left (3+e^{2 x}+x\right )}{\left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx\\ &=\left (20 e^4\right ) \int \left (-\frac {5}{\left (3+e^{2 x}+x\right ) \left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3}-\frac {2 x}{\left (3+e^{2 x}+x\right ) \left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3}\right ) \, dx+\int \left (1+\frac {10 \left (-1+4 e^4\right )}{\left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3}\right ) \, dx-\operatorname {Subst}\left (\int \frac {1}{x (1+x)} \, dx,x,e^x\right )\\ &=x-\left (40 e^4\right ) \int \frac {x}{\left (3+e^{2 x}+x\right ) \left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx-\left (100 e^4\right ) \int \frac {1}{\left (3+e^{2 x}+x\right ) \left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx-\left (10 \left (1-4 e^4\right )\right ) \int \frac {1}{\left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,e^x\right )+\operatorname {Subst}\left (\int \frac {1}{1+x} \, dx,x,e^x\right )\\ &=\log \left (1+e^x\right )-\left (40 e^4\right ) \int \frac {x}{\left (3+e^{2 x}+x\right ) \left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx-\left (100 e^4\right ) \int \frac {1}{\left (3+e^{2 x}+x\right ) \left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx-\left (10 \left (1-4 e^4\right )\right ) \int \frac {1}{\left (x-2 e^4 \log \left (3+e^{2 x}+x\right )\right )^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.15, size = 29, normalized size = 1.00 \begin {gather*} \log \left (1+e^x\right )+\frac {5}{\left (-x+2 e^4 \log \left (3+e^{2 x}+x\right )\right )^2} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(30 - 20*E^4 + E^(2*x)*(10 - 40*E^4) + 10*x + E^(3*x)*(10 - 40*E^4 - x^3) + E^x*(30 - 20*E^4 + 10*x

- 3*x^3 - x^4) + (6*E^(4 + 3*x)*x^2 + E^(4 + x)*(18*x^2 + 6*x^3))*Log[3 + E^(2*x) + x] + (-12*E^(8 + 3*x)*x +

E^(8 + x)*(-36*x - 12*x^2))*Log[3 + E^(2*x) + x]^2 + (8*E^(12 + 3*x) + E^(12 + x)*(24 + 8*x))*Log[3 + E^(2*x)

+ x]^3)/(-3*x^3 - E^(2*x)*x^3 - E^(3*x)*x^3 - x^4 + E^x*(-3*x^3 - x^4) + (6*E^(4 + 2*x)*x^2 + 6*E^(4 + 3*x)*x^

2 + E^4*(18*x^2 + 6*x^3) + E^(4 + x)*(18*x^2 + 6*x^3))*Log[3 + E^(2*x) + x] + (-12*E^(8 + 2*x)*x - 12*E^(8 + 3

*x)*x + E^8*(-36*x - 12*x^2) + E^(8 + x)*(-36*x - 12*x^2))*Log[3 + E^(2*x) + x]^2 + (8*E^(12 + 2*x) + 8*E^(12

+ 3*x) + E^12*(24 + 8*x) + E^(12 + x)*(24 + 8*x))*Log[3 + E^(2*x) + x]^3),x]

[Out]

Log[1 + E^x] + 5/(-x + 2*E^4*Log[3 + E^(2*x) + x])^2

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fricas [B] time = 0.86, size = 130, normalized size = 4.48 \begin {gather*} \frac {4 \, x e^{4} \log \left ({\left ({\left (x + 3\right )} e^{24} + e^{\left (2 \, x + 24\right )}\right )} e^{\left (-24\right )}\right ) \log \left (e^{12} + e^{\left (x + 12\right )}\right ) - 4 \, e^{8} \log \left ({\left ({\left (x + 3\right )} e^{24} + e^{\left (2 \, x + 24\right )}\right )} e^{\left (-24\right )}\right )^{2} \log \left (e^{12} + e^{\left (x + 12\right )}\right ) - x^{2} \log \left (e^{12} + e^{\left (x + 12\right )}\right ) - 5}{4 \, x e^{4} \log \left ({\left ({\left (x + 3\right )} e^{24} + e^{\left (2 \, x + 24\right )}\right )} e^{\left (-24\right )}\right ) - 4 \, e^{8} \log \left ({\left ({\left (x + 3\right )} e^{24} + e^{\left (2 \, x + 24\right )}\right )} e^{\left (-24\right )}\right )^{2} - x^{2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*exp(4)^3*exp(x)^3+(8*x+24)*exp(4)^3*exp(x))*log(exp(x)^2+3+x)^3+(-12*x*exp(4)^2*exp(x)^3+(-12*x^

2-36*x)*exp(4)^2*exp(x))*log(exp(x)^2+3+x)^2+(6*x^2*exp(4)*exp(x)^3+(6*x^3+18*x^2)*exp(4)*exp(x))*log(exp(x)^2

+3+x)+(-40*exp(4)-x^3+10)*exp(x)^3+(-40*exp(4)+10)*exp(x)^2+(-20*exp(4)-x^4-3*x^3+10*x+30)*exp(x)-20*exp(4)+10

*x+30)/((8*exp(4)^3*exp(x)^3+8*exp(4)^3*exp(x)^2+(8*x+24)*exp(4)^3*exp(x)+(8*x+24)*exp(4)^3)*log(exp(x)^2+3+x)

^3+(-12*x*exp(4)^2*exp(x)^3-12*x*exp(4)^2*exp(x)^2+(-12*x^2-36*x)*exp(4)^2*exp(x)+(-12*x^2-36*x)*exp(4)^2)*log

(exp(x)^2+3+x)^2+(6*x^2*exp(4)*exp(x)^3+6*x^2*exp(4)*exp(x)^2+(6*x^3+18*x^2)*exp(4)*exp(x)+(6*x^3+18*x^2)*exp(

4))*log(exp(x)^2+3+x)-x^3*exp(x)^3-exp(x)^2*x^3+(-x^4-3*x^3)*exp(x)-x^4-3*x^3),x, algorithm="fricas")

[Out]

(4*x*e^4*log(((x + 3)*e^24 + e^(2*x + 24))*e^(-24))*log(e^12 + e^(x + 12)) - 4*e^8*log(((x + 3)*e^24 + e^(2*x

+ 24))*e^(-24))^2*log(e^12 + e^(x + 12)) - x^2*log(e^12 + e^(x + 12)) - 5)/(4*x*e^4*log(((x + 3)*e^24 + e^(2*x

+ 24))*e^(-24)) - 4*e^8*log(((x + 3)*e^24 + e^(2*x + 24))*e^(-24))^2 - x^2)

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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(((8*exp(4)^3*exp(x)^3+(8*x+24)*exp(4)^3*exp(x))*log(exp(x)^2+3+x)^3+(-12*x*exp(4)^2*exp(x)^3+(-12*x^

2-36*x)*exp(4)^2*exp(x))*log(exp(x)^2+3+x)^2+(6*x^2*exp(4)*exp(x)^3+(6*x^3+18*x^2)*exp(4)*exp(x))*log(exp(x)^2

+3+x)+(-40*exp(4)-x^3+10)*exp(x)^3+(-40*exp(4)+10)*exp(x)^2+(-20*exp(4)-x^4-3*x^3+10*x+30)*exp(x)-20*exp(4)+10

*x+30)/((8*exp(4)^3*exp(x)^3+8*exp(4)^3*exp(x)^2+(8*x+24)*exp(4)^3*exp(x)+(8*x+24)*exp(4)^3)*log(exp(x)^2+3+x)

^3+(-12*x*exp(4)^2*exp(x)^3-12*x*exp(4)^2*exp(x)^2+(-12*x^2-36*x)*exp(4)^2*exp(x)+(-12*x^2-36*x)*exp(4)^2)*log

(exp(x)^2+3+x)^2+(6*x^2*exp(4)*exp(x)^3+6*x^2*exp(4)*exp(x)^2+(6*x^3+18*x^2)*exp(4)*exp(x)+(6*x^3+18*x^2)*exp(

4))*log(exp(x)^2+3+x)-x^3*exp(x)^3-exp(x)^2*x^3+(-x^4-3*x^3)*exp(x)-x^4-3*x^3),x, algorithm="giac")

[Out]

Timed out

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maple [A] time = 0.10, size = 27, normalized size = 0.93


method	result	size

risch	\(\frac {5}{\left (2 \ln \left ({\mathrm e}^{2 x}+3+x \right ) {\mathrm e}^{4}-x \right )^{2}}+\ln \left ({\mathrm e}^{x}+1\right )\)	\(27\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((8*exp(4)^3*exp(x)^3+(8*x+24)*exp(4)^3*exp(x))*ln(exp(x)^2+3+x)^3+(-12*x*exp(4)^2*exp(x)^3+(-12*x^2-36*x)

*exp(4)^2*exp(x))*ln(exp(x)^2+3+x)^2+(6*x^2*exp(4)*exp(x)^3+(6*x^3+18*x^2)*exp(4)*exp(x))*ln(exp(x)^2+3+x)+(-4

0*exp(4)-x^3+10)*exp(x)^3+(-40*exp(4)+10)*exp(x)^2+(-20*exp(4)-x^4-3*x^3+10*x+30)*exp(x)-20*exp(4)+10*x+30)/((

8*exp(4)^3*exp(x)^3+8*exp(4)^3*exp(x)^2+(8*x+24)*exp(4)^3*exp(x)+(8*x+24)*exp(4)^3)*ln(exp(x)^2+3+x)^3+(-12*x*

exp(4)^2*exp(x)^3-12*x*exp(4)^2*exp(x)^2+(-12*x^2-36*x)*exp(4)^2*exp(x)+(-12*x^2-36*x)*exp(4)^2)*ln(exp(x)^2+3

+x)^2+(6*x^2*exp(4)*exp(x)^3+6*x^2*exp(4)*exp(x)^2+(6*x^3+18*x^2)*exp(4)*exp(x)+(6*x^3+18*x^2)*exp(4))*ln(exp(

x)^2+3+x)-x^3*exp(x)^3-exp(x)^2*x^3+(-x^4-3*x^3)*exp(x)-x^4-3*x^3),x,method=_RETURNVERBOSE)

[Out]

5/(2*ln(exp(2*x)+3+x)*exp(4)-x)^2+ln(exp(x)+1)

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maxima [A] time = 1.11, size = 43, normalized size = 1.48 \begin {gather*} -\frac {5}{4 \, x e^{4} \log \left (x + e^{\left (2 \, x\right )} + 3\right ) - 4 \, e^{8} \log \left (x + e^{\left (2 \, x\right )} + 3\right )^{2} - x^{2}} + \log \left (e^{x} + 1\right ) \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*exp(4)^3*exp(x)^3+(8*x+24)*exp(4)^3*exp(x))*log(exp(x)^2+3+x)^3+(-12*x*exp(4)^2*exp(x)^3+(-12*x^

2-36*x)*exp(4)^2*exp(x))*log(exp(x)^2+3+x)^2+(6*x^2*exp(4)*exp(x)^3+(6*x^3+18*x^2)*exp(4)*exp(x))*log(exp(x)^2

+3+x)+(-40*exp(4)-x^3+10)*exp(x)^3+(-40*exp(4)+10)*exp(x)^2+(-20*exp(4)-x^4-3*x^3+10*x+30)*exp(x)-20*exp(4)+10

*x+30)/((8*exp(4)^3*exp(x)^3+8*exp(4)^3*exp(x)^2+(8*x+24)*exp(4)^3*exp(x)+(8*x+24)*exp(4)^3)*log(exp(x)^2+3+x)

^3+(-12*x*exp(4)^2*exp(x)^3-12*x*exp(4)^2*exp(x)^2+(-12*x^2-36*x)*exp(4)^2*exp(x)+(-12*x^2-36*x)*exp(4)^2)*log

(exp(x)^2+3+x)^2+(6*x^2*exp(4)*exp(x)^3+6*x^2*exp(4)*exp(x)^2+(6*x^3+18*x^2)*exp(4)*exp(x)+(6*x^3+18*x^2)*exp(

4))*log(exp(x)^2+3+x)-x^3*exp(x)^3-exp(x)^2*x^3+(-x^4-3*x^3)*exp(x)-x^4-3*x^3),x, algorithm="maxima")

[Out]

-5/(4*x*e^4*log(x + e^(2*x) + 3) - 4*e^8*log(x + e^(2*x) + 3)^2 - x^2) + log(e^x + 1)

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mupad [B] time = 0.52, size = 24, normalized size = 0.83 \begin {gather*} \ln \left ({\mathrm {e}}^x+1\right )+\frac {5}{{\left (x-2\,{\mathrm {e}}^4\,\ln \left (x+{\mathrm {e}}^{2\,x}+3\right )\right )}^2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((20*exp(4) - 10*x + log(x + exp(2*x) + 3)^2*(exp(8)*exp(x)*(36*x + 12*x^2) + 12*x*exp(3*x)*exp(8)) + exp(x

)*(20*exp(4) - 10*x + 3*x^3 + x^4 - 30) - log(x + exp(2*x) + 3)^3*(8*exp(3*x)*exp(12) + exp(12)*exp(x)*(8*x +

24)) - log(x + exp(2*x) + 3)*(exp(4)*exp(x)*(18*x^2 + 6*x^3) + 6*x^2*exp(3*x)*exp(4)) + exp(3*x)*(40*exp(4) +

x^3 - 10) + exp(2*x)*(40*exp(4) - 10) - 30)/(x^3*exp(2*x) + x^3*exp(3*x) - log(x + exp(2*x) + 3)^3*(8*exp(2*x)

*exp(12) + 8*exp(3*x)*exp(12) + exp(12)*(8*x + 24) + exp(12)*exp(x)*(8*x + 24)) + exp(x)*(3*x^3 + x^4) + log(x

+ exp(2*x) + 3)^2*(exp(8)*(36*x + 12*x^2) + exp(8)*exp(x)*(36*x + 12*x^2) + 12*x*exp(2*x)*exp(8) + 12*x*exp(3

*x)*exp(8)) + 3*x^3 + x^4 - log(x + exp(2*x) + 3)*(exp(4)*(18*x^2 + 6*x^3) + exp(4)*exp(x)*(18*x^2 + 6*x^3) +

6*x^2*exp(2*x)*exp(4) + 6*x^2*exp(3*x)*exp(4))),x)

[Out]

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

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sympy [A] time = 0.49, size = 44, normalized size = 1.52 \begin {gather*} \log {\left (e^{x} + 1 \right )} + \frac {5}{x^{2} - 4 x e^{4} \log {\left (x + e^{2 x} + 3 \right )} + 4 e^{8} \log {\left (x + e^{2 x} + 3 \right )}^{2}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((8*exp(4)**3*exp(x)**3+(8*x+24)*exp(4)**3*exp(x))*ln(exp(x)**2+3+x)**3+(-12*x*exp(4)**2*exp(x)**3+(

-12*x**2-36*x)*exp(4)**2*exp(x))*ln(exp(x)**2+3+x)**2+(6*x**2*exp(4)*exp(x)**3+(6*x**3+18*x**2)*exp(4)*exp(x))

*ln(exp(x)**2+3+x)+(-40*exp(4)-x**3+10)*exp(x)**3+(-40*exp(4)+10)*exp(x)**2+(-20*exp(4)-x**4-3*x**3+10*x+30)*e

xp(x)-20*exp(4)+10*x+30)/((8*exp(4)**3*exp(x)**3+8*exp(4)**3*exp(x)**2+(8*x+24)*exp(4)**3*exp(x)+(8*x+24)*exp(

4)**3)*ln(exp(x)**2+3+x)**3+(-12*x*exp(4)**2*exp(x)**3-12*x*exp(4)**2*exp(x)**2+(-12*x**2-36*x)*exp(4)**2*exp(

x)+(-12*x**2-36*x)*exp(4)**2)*ln(exp(x)**2+3+x)**2+(6*x**2*exp(4)*exp(x)**3+6*x**2*exp(4)*exp(x)**2+(6*x**3+18

*x**2)*exp(4)*exp(x)+(6*x**3+18*x**2)*exp(4))*ln(exp(x)**2+3+x)-x**3*exp(x)**3-exp(x)**2*x**3+(-x**4-3*x**3)*e

xp(x)-x**4-3*x**3),x)

[Out]

log(exp(x) + 1) + 5/(x**2 - 4*x*exp(4)*log(x + exp(2*x) + 3) + 4*exp(8)*log(x + exp(2*x) + 3)**2)

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