3.102.6 \(\int \frac {8+16 x+10 x^2+2 x^3+e^{3 e^{25^{\frac {2 (3+x)}{6+3 x}}+2\ 25^{\frac {3+x}{6+3 x}} x+x^2}} (4+4 x+x^2+e^{25^{\frac {2 (3+x)}{6+3 x}}+2\ 25^{\frac {3+x}{6+3 x}} x+x^2} (24 x^2+24 x^3+6 x^4-2\ 25^{\frac {2 (3+x)}{6+3 x}} x \log (25)+25^{\frac {3+x}{6+3 x}} (24 x+24 x^2+6 x^3-2 x^2 \log (25))))}{4+4 x+x^2} \, dx\)

Optimal. Leaf size=28 \[ x \left (2+e^{3 e^{\left (25^{\frac {1}{2+\frac {x}{3+x}}}+x\right )^2}}+x\right ) \]

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Rubi [F]  time = 69.36, 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 {8+16 x+10 x^2+2 x^3+\exp \left (3 \exp \left (25^{\frac {2 (3+x)}{6+3 x}}+2\ 25^{\frac {3+x}{6+3 x}} x+x^2\right )\right ) \left (4+4 x+x^2+\exp \left (25^{\frac {2 (3+x)}{6+3 x}}+2\ 25^{\frac {3+x}{6+3 x}} x+x^2\right ) \left (24 x^2+24 x^3+6 x^4-2\ 25^{\frac {2 (3+x)}{6+3 x}} x \log (25)+25^{\frac {3+x}{6+3 x}} \left (24 x+24 x^2+6 x^3-2 x^2 \log (25)\right )\right )\right )}{4+4 x+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(8 + 16*x + 10*x^2 + 2*x^3 + E^(3*E^(25^((2*(3 + x))/(6 + 3*x)) + 2*25^((3 + x)/(6 + 3*x))*x + x^2))*(4 +
4*x + x^2 + E^(25^((2*(3 + x))/(6 + 3*x)) + 2*25^((3 + x)/(6 + 3*x))*x + x^2)*(24*x^2 + 24*x^3 + 6*x^4 - 2*25^
((2*(3 + x))/(6 + 3*x))*x*Log[25] + 25^((3 + x)/(6 + 3*x))*(24*x + 24*x^2 + 6*x^3 - 2*x^2*Log[25]))))/(4 + 4*x
+ x^2),x]

[Out]

2*x + x^2 + Defer[Int][E^(3*E^(25^((3 + x)/(6 + 3*x)) + x)^2), x] - 2*Log[25]*Defer[Int][5^((2*(3 + x))/(3*(2
+ x)))*E^(3*E^(25^((3 + x)/(6 + 3*x)) + x)^2 + (25^((3 + x)/(6 + 3*x)) + x)^2), x] + 6*Defer[Int][5^((2*(3 + x
))/(3*(2 + x)))*E^(3*E^(25^((3 + x)/(6 + 3*x)) + x)^2 + (25^((3 + x)/(6 + 3*x)) + x)^2)*x, x] + 6*Defer[Int][E
^(3*E^(25^((3 + x)/(6 + 3*x)) + x)^2 + (25^((3 + x)/(6 + 3*x)) + x)^2)*x^2, x] - 8*Log[25]*Defer[Int][(5^((2*(
3 + x))/(3*(2 + x)))*E^(3*E^(25^((3 + x)/(6 + 3*x)) + x)^2 + (25^((3 + x)/(6 + 3*x)) + x)^2))/(2 + x)^2, x] +
4*Log[25]*Defer[Int][(5^((4*(3 + x))/(3*(2 + x)))*E^(3*E^(25^((3 + x)/(6 + 3*x)) + x)^2 + (25^((3 + x)/(6 + 3*
x)) + x)^2))/(2 + x)^2, x] + 8*Log[25]*Defer[Int][(5^((2*(3 + x))/(3*(2 + x)))*E^(3*E^(25^((3 + x)/(6 + 3*x))
+ x)^2 + (25^((3 + x)/(6 + 3*x)) + x)^2))/(2 + x), x] - 2*Log[25]*Defer[Int][(5^((4*(3 + x))/(3*(2 + x)))*E^(3
*E^(25^((3 + x)/(6 + 3*x)) + x)^2 + (25^((3 + x)/(6 + 3*x)) + x)^2))/(2 + x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8+16 x+10 x^2+2 x^3+\exp \left (3 \exp \left (25^{\frac {2 (3+x)}{6+3 x}}+2\ 25^{\frac {3+x}{6+3 x}} x+x^2\right )\right ) \left (4+4 x+x^2+\exp \left (25^{\frac {2 (3+x)}{6+3 x}}+2\ 25^{\frac {3+x}{6+3 x}} x+x^2\right ) \left (24 x^2+24 x^3+6 x^4-2\ 25^{\frac {2 (3+x)}{6+3 x}} x \log (25)+25^{\frac {3+x}{6+3 x}} \left (24 x+24 x^2+6 x^3-2 x^2 \log (25)\right )\right )\right )}{(2+x)^2} \, dx\\ &=\int \frac {8+16 x+10 x^2+2 x^3+e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}} \left (4+4 x+x^2+2 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2} x \left (25^{\frac {3+x}{6+3 x}}+x\right ) \left (12+12 x+3 x^2-25^{\frac {3+x}{6+3 x}} \log (25)\right )\right )}{(2+x)^2} \, dx\\ &=\int \left (\frac {8}{(2+x)^2}+\frac {4 e^{3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}}}{(2+x)^2}+\frac {16 x}{(2+x)^2}+\frac {4 e^{3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}} x}{(2+x)^2}+\frac {10 x^2}{(2+x)^2}+\frac {e^{3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}} x^2}{(2+x)^2}+\frac {2 x^3}{(2+x)^2}+\frac {2 \exp \left (3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2\right ) x \left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right ) \left (12+12 x+3 x^2-25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}} \log (25)\right )}{(2+x)^2}\right ) \, dx\\ &=-\frac {8}{2+x}+2 \int \frac {x^3}{(2+x)^2} \, dx+2 \int \frac {\exp \left (3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2\right ) x \left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right ) \left (12+12 x+3 x^2-25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}} \log (25)\right )}{(2+x)^2} \, dx+4 \int \frac {e^{3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx+4 \int \frac {e^{3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}} x}{(2+x)^2} \, dx+10 \int \frac {x^2}{(2+x)^2} \, dx+16 \int \frac {x}{(2+x)^2} \, dx+\int \frac {e^{3 e^{\left (25^{\frac {3}{6+3 x}+\frac {x}{6+3 x}}+x\right )^2}} x^2}{(2+x)^2} \, dx\\ &=-\frac {8}{2+x}+2 \int \left (-4+x-\frac {8}{(2+x)^2}+\frac {12}{2+x}\right ) \, dx+2 \int \frac {\exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x \left (25^{\frac {3+x}{6+3 x}}+x\right ) \left (12+12 x+3 x^2-25^{\frac {3+x}{6+3 x}} \log (25)\right )}{(2+x)^2} \, dx+4 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx+4 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}} x}{(2+x)^2} \, dx+10 \int \left (1+\frac {4}{(2+x)^2}-\frac {4}{2+x}\right ) \, dx+16 \int \left (-\frac {2}{(2+x)^2}+\frac {1}{2+x}\right ) \, dx+\int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}} x^2}{(2+x)^2} \, dx\\ &=2 x+x^2+2 \int \left (3 \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x^2+\frac {5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x \left (12+3 x^2+x (12-\log (25))\right )}{(2+x)^2}-\frac {5^{\frac {4 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x \log (25)}{(2+x)^2}\right ) \, dx+4 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx+4 \int \left (-\frac {2 e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2}+\frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{2+x}\right ) \, dx+\int \left (e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}+\frac {4 e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2}-\frac {4 e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{2+x}\right ) \, dx\\ &=2 x+x^2+2 \int \frac {5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x \left (12+3 x^2+x (12-\log (25))\right )}{(2+x)^2} \, dx+2 \left (4 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx\right )+6 \int \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x^2 \, dx-8 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx-(2 \log (25)) \int \frac {5^{\frac {4 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x}{(2+x)^2} \, dx+\int e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}} \, dx\\ &=2 x+x^2+2 \int \left (3\ 5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x-5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) \log (25)-\frac {4\ 5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) \log (25)}{(2+x)^2}+\frac {4\ 5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) \log (25)}{2+x}\right ) \, dx+2 \left (4 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx\right )+6 \int \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x^2 \, dx-8 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx-(2 \log (25)) \int \left (-\frac {2\ 5^{\frac {4 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right )}{(2+x)^2}+\frac {5^{\frac {4 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right )}{2+x}\right ) \, dx+\int e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}} \, dx\\ &=2 x+x^2+2 \left (4 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx\right )+6 \int 5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x \, dx+6 \int \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) x^2 \, dx-8 \int \frac {e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}}}{(2+x)^2} \, dx-(2 \log (25)) \int 5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right ) \, dx-(2 \log (25)) \int \frac {5^{\frac {4 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right )}{2+x} \, dx+(4 \log (25)) \int \frac {5^{\frac {4 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right )}{(2+x)^2} \, dx-(8 \log (25)) \int \frac {5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right )}{(2+x)^2} \, dx+(8 \log (25)) \int \frac {5^{\frac {2 (3+x)}{3 (2+x)}} \exp \left (3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}+\left (25^{\frac {3+x}{6+3 x}}+x\right )^2\right )}{2+x} \, dx+\int e^{3 e^{\left (25^{\frac {3+x}{6+3 x}}+x\right )^2}} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.55, size = 29, normalized size = 1.04 \begin {gather*} x \left (2+e^{3 e^{\left (5^{\frac {2 (3+x)}{3 (2+x)}}+x\right )^2}}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(8 + 16*x + 10*x^2 + 2*x^3 + E^(3*E^(25^((2*(3 + x))/(6 + 3*x)) + 2*25^((3 + x)/(6 + 3*x))*x + x^2))
*(4 + 4*x + x^2 + E^(25^((2*(3 + x))/(6 + 3*x)) + 2*25^((3 + x)/(6 + 3*x))*x + x^2)*(24*x^2 + 24*x^3 + 6*x^4 -
2*25^((2*(3 + x))/(6 + 3*x))*x*Log[25] + 25^((3 + x)/(6 + 3*x))*(24*x + 24*x^2 + 6*x^3 - 2*x^2*Log[25]))))/(4
+ 4*x + x^2),x]

[Out]

x*(2 + E^(3*E^(5^((2*(3 + x))/(3*(2 + x))) + x)^2) + x)

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fricas [A]  time = 1.03, size = 44, normalized size = 1.57 \begin {gather*} x^{2} + x e^{\left (3 \, e^{\left (2 \cdot 5^{\frac {2 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}} x + x^{2} + 5^{\frac {4 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}}\right )}\right )} + 2 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x*log(5)*exp(2*(3+x)*log(5)/(6+3*x))^2+(-4*x^2*log(5)+6*x^3+24*x^2+24*x)*exp(2*(3+x)*log(5)/(6
+3*x))+6*x^4+24*x^3+24*x^2)*exp(exp(2*(3+x)*log(5)/(6+3*x))^2+2*x*exp(2*(3+x)*log(5)/(6+3*x))+x^2)+x^2+4*x+4)*
exp(3*exp(exp(2*(3+x)*log(5)/(6+3*x))^2+2*x*exp(2*(3+x)*log(5)/(6+3*x))+x^2))+2*x^3+10*x^2+16*x+8)/(x^2+4*x+4)
,x, algorithm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, x^{3} + 10 \, x^{2} + {\left (x^{2} + 2 \, {\left (3 \, x^{4} + 12 \, x^{3} - 2 \cdot 5^{\frac {4 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}} x \log \relax (5) + {\left (3 \, x^{3} - 2 \, x^{2} \log \relax (5) + 12 \, x^{2} + 12 \, x\right )} 5^{\frac {2 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}} + 12 \, x^{2}\right )} e^{\left (2 \cdot 5^{\frac {2 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}} x + x^{2} + 5^{\frac {4 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}}\right )} + 4 \, x + 4\right )} e^{\left (3 \, e^{\left (2 \cdot 5^{\frac {2 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}} x + x^{2} + 5^{\frac {4 \, {\left (x + 3\right )}}{3 \, {\left (x + 2\right )}}}\right )}\right )} + 16 \, x + 8}{x^{2} + 4 \, x + 4}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x*log(5)*exp(2*(3+x)*log(5)/(6+3*x))^2+(-4*x^2*log(5)+6*x^3+24*x^2+24*x)*exp(2*(3+x)*log(5)/(6
+3*x))+6*x^4+24*x^3+24*x^2)*exp(exp(2*(3+x)*log(5)/(6+3*x))^2+2*x*exp(2*(3+x)*log(5)/(6+3*x))+x^2)+x^2+4*x+4)*
exp(3*exp(exp(2*(3+x)*log(5)/(6+3*x))^2+2*x*exp(2*(3+x)*log(5)/(6+3*x))+x^2))+2*x^3+10*x^2+16*x+8)/(x^2+4*x+4)
,x, algorithm="giac")

[Out]

integrate((2*x^3 + 10*x^2 + (x^2 + 2*(3*x^4 + 12*x^3 - 2*5^(4/3*(x + 3)/(x + 2))*x*log(5) + (3*x^3 - 2*x^2*log
(5) + 12*x^2 + 12*x)*5^(2/3*(x + 3)/(x + 2)) + 12*x^2)*e^(2*5^(2/3*(x + 3)/(x + 2))*x + x^2 + 5^(4/3*(x + 3)/(
x + 2))) + 4*x + 4)*e^(3*e^(2*5^(2/3*(x + 3)/(x + 2))*x + x^2 + 5^(4/3*(x + 3)/(x + 2)))) + 16*x + 8)/(x^2 + 4
*x + 4), x)

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maple [A]  time = 0.18, size = 30, normalized size = 1.07

method	result	size
risch	\(x^{2}+x \,{\mathrm e}^{3 \,{\mathrm e}^{\left (5^{\frac {2+\frac {2 x}{3}}{2+x}}+x \right )^{2}}}+2 x\)	\(30\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x*ln(5)*exp(2*(3+x)*ln(5)/(6+3*x))^2+(-4*x^2*ln(5)+6*x^3+24*x^2+24*x)*exp(2*(3+x)*ln(5)/(6+3*x))+6*x
^4+24*x^3+24*x^2)*exp(exp(2*(3+x)*ln(5)/(6+3*x))^2+2*x*exp(2*(3+x)*ln(5)/(6+3*x))+x^2)+x^2+4*x+4)*exp(3*exp(ex
p(2*(3+x)*ln(5)/(6+3*x))^2+2*x*exp(2*(3+x)*ln(5)/(6+3*x))+x^2))+2*x^3+10*x^2+16*x+8)/(x^2+4*x+4),x,method=_RET
URNVERBOSE)

[Out]

x^2+x*exp(3*exp((5^(2/3*(3+x)/(2+x))+x)^2))+2*x

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x^{2} + x e^{\left (3 \, e^{\left (2 \cdot 5^{\frac {2}{3}} 5^{\frac {2}{3 \, {\left (x + 2\right )}}} x + x^{2} + 5 \cdot 5^{\frac {1}{3}} 5^{\frac {4}{3 \, {\left (x + 2\right )}}}\right )}\right )} + 2 \, x - \int 0\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x*log(5)*exp(2*(3+x)*log(5)/(6+3*x))^2+(-4*x^2*log(5)+6*x^3+24*x^2+24*x)*exp(2*(3+x)*log(5)/(6
+3*x))+6*x^4+24*x^3+24*x^2)*exp(exp(2*(3+x)*log(5)/(6+3*x))^2+2*x*exp(2*(3+x)*log(5)/(6+3*x))+x^2)+x^2+4*x+4)*
exp(3*exp(exp(2*(3+x)*log(5)/(6+3*x))^2+2*x*exp(2*(3+x)*log(5)/(6+3*x))+x^2))+2*x^3+10*x^2+16*x+8)/(x^2+4*x+4)
,x, algorithm="maxima")

[Out]

x^2 + x*e^(3*e^(2*5^(2/3)*5^(2/3/(x + 2))*x + x^2 + 5*5^(1/3)*5^(4/3/(x + 2)))) + 2*x - integrate(0, x)

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mupad [B]  time = 9.75, size = 45, normalized size = 1.61 \begin {gather*} x\,\left (x+{\mathrm {e}}^{3\,{\mathrm {e}}^{2\,5^{\frac {2\,\left (x+3\right )}{3\,\left (x+2\right )}}\,x}\,{\mathrm {e}}^{5^{\frac {4\,\left (x+3\right )}{3\,\left (x+2\right )}}}\,{\mathrm {e}}^{x^2}}+2\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((16*x + exp(3*exp(exp((4*log(5)*(x + 3))/(3*x + 6)) + 2*x*exp((2*log(5)*(x + 3))/(3*x + 6)) + x^2))*(4*x +
exp(exp((4*log(5)*(x + 3))/(3*x + 6)) + 2*x*exp((2*log(5)*(x + 3))/(3*x + 6)) + x^2)*(exp((2*log(5)*(x + 3))/
(3*x + 6))*(24*x - 4*x^2*log(5) + 24*x^2 + 6*x^3) + 24*x^2 + 24*x^3 + 6*x^4 - 4*x*exp((4*log(5)*(x + 3))/(3*x
+ 6))*log(5)) + x^2 + 4) + 10*x^2 + 2*x^3 + 8)/(4*x + x^2 + 4),x)

[Out]

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

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sympy [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((((-4*x*ln(5)*exp(2*(3+x)*ln(5)/(6+3*x))**2+(-4*x**2*ln(5)+6*x**3+24*x**2+24*x)*exp(2*(3+x)*ln(5)/(6
+3*x))+6*x**4+24*x**3+24*x**2)*exp(exp(2*(3+x)*ln(5)/(6+3*x))**2+2*x*exp(2*(3+x)*ln(5)/(6+3*x))+x**2)+x**2+4*x
+4)*exp(3*exp(exp(2*(3+x)*ln(5)/(6+3*x))**2+2*x*exp(2*(3+x)*ln(5)/(6+3*x))+x**2))+2*x**3+10*x**2+16*x+8)/(x**2
+4*x+4),x)

[Out]

Timed out

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