3.69.88 \(\int \frac {3 x^2+x^3+e^{x+x^2} (-6 x+6 x^2+21 x^3+6 x^4)+(6 x+2 x^2+e^{x+x^2} (9 x+21 x^2+6 x^3)) \log (\frac {2}{e^{5/3} (3+x)})+(3+x) \log ^2(\frac {2}{e^{5/3} (3+x)})}{3 x^3+x^4+(6 x^2+2 x^3) \log (\frac {2}{e^{5/3} (3+x)})+(3 x+x^2) \log ^2(\frac {2}{e^{5/3} (3+x)})} \, dx\)

Optimal. Leaf size=30 \[ 2+\log (x)+\frac {3 e^{x+x^2}}{x+\log \left (\frac {2}{e^{5/3} (3+x)}\right )} \]

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Rubi [F]  time = 13.39, 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 {3 x^2+x^3+e^{x+x^2} \left (-6 x+6 x^2+21 x^3+6 x^4\right )+\left (6 x+2 x^2+e^{x+x^2} \left (9 x+21 x^2+6 x^3\right )\right ) \log \left (\frac {2}{e^{5/3} (3+x)}\right )+(3+x) \log ^2\left (\frac {2}{e^{5/3} (3+x)}\right )}{3 x^3+x^4+\left (6 x^2+2 x^3\right ) \log \left (\frac {2}{e^{5/3} (3+x)}\right )+\left (3 x+x^2\right ) \log ^2\left (\frac {2}{e^{5/3} (3+x)}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(3*x^2 + x^3 + E^(x + x^2)*(-6*x + 6*x^2 + 21*x^3 + 6*x^4) + (6*x + 2*x^2 + E^(x + x^2)*(9*x + 21*x^2 + 6*
x^3))*Log[2/(E^(5/3)*(3 + x))] + (3 + x)*Log[2/(E^(5/3)*(3 + x))]^2)/(3*x^3 + x^4 + (6*x^2 + 2*x^3)*Log[2/(E^(
5/3)*(3 + x))] + (3*x + x^2)*Log[2/(E^(5/3)*(3 + x))]^2),x]

[Out]

Log[x] + 6*Defer[Int][(-3*x + 5*(1 - (3*Log[2])/5) - 3*Log[(3 + x)^(-1)])^(-1), x] - 27*Defer[Int][E^(x + x^2)
/(3*x - 5*(1 - (3*Log[2])/5) + 3*Log[(3 + x)^(-1)])^2, x] + 81*Defer[Int][1/((-3 - x)*(3*x - 5*(1 - (3*Log[2])
/5) + 3*Log[(3 + x)^(-1)])^2), x] + 81*Defer[Int][1/((3 + x)*(3*x - 5*(1 - (3*Log[2])/5) + 3*Log[(3 + x)^(-1)]
)^2), x] + 27*Defer[Int][E^(x + x^2)/((3 + x)*(3*x - 5*(1 - (3*Log[2])/5) + 3*Log[(3 + x)^(-1)])^2), x] + 6*De
fer[Int][(3*x - 5*(1 - (3*Log[2])/5) + 3*Log[(3 + x)^(-1)])^(-1), x] + 9*Defer[Int][E^(x + x^2)/(3*x - 5*(1 -
(3*Log[2])/5) + 3*Log[(3 + x)^(-1)]), x] + 18*Defer[Int][(E^(x + x^2)*x)/(3*x - 5*(1 - (3*Log[2])/5) + 3*Log[(
3 + x)^(-1)]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 x^2+x^3+3 e^{x+x^2} x \left (-2+2 x+7 x^2+2 x^3\right )+x (3+x) \left (2+e^{x+x^2} (3+6 x)\right ) \left (-\frac {5}{3}+\log (2)+\log \left (\frac {1}{3+x}\right )\right )+(3+x) \left (-\frac {5}{3}+\log (2)+\log \left (\frac {1}{3+x}\right )\right )^2}{x (3+x) \left (x-\frac {5}{3} \left (1-\frac {3 \log (2)}{5}\right )+\log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ &=\int \frac {9 \left (3 x^2+x^3+3 e^{x+x^2} x \left (-2+2 x+7 x^2+2 x^3\right )+x (3+x) \left (2+e^{x+x^2} (3+6 x)\right ) \left (-\frac {5}{3}+\log (2)+\log \left (\frac {1}{3+x}\right )\right )+(3+x) \left (-\frac {5}{3}+\log (2)+\log \left (\frac {1}{3+x}\right )\right )^2\right )}{x (3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ &=9 \int \frac {3 x^2+x^3+3 e^{x+x^2} x \left (-2+2 x+7 x^2+2 x^3\right )+x (3+x) \left (2+e^{x+x^2} (3+6 x)\right ) \left (-\frac {5}{3}+\log (2)+\log \left (\frac {1}{3+x}\right )\right )+(3+x) \left (-\frac {5}{3}+\log (2)+\log \left (\frac {1}{3+x}\right )\right )^2}{x (3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ &=9 \int \left (\frac {3 x}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {x^2}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {\left (5 \left (1-\frac {3 \log (2)}{5}\right )-3 \log \left (\frac {1}{3+x}\right )\right )^2}{9 x \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {-10 \left (1-\frac {3 \log (2)}{5}\right )+6 \log \left (\frac {1}{3+x}\right )}{3 \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {e^{x+x^2} \left (6 x^3-29 x \left (1-\frac {21 \log (2)}{29}\right )-21 \left (1-\frac {3 \log (2)}{7}\right )+11 x^2 \left (1+\frac {6 \log (2)}{11}\right )+9 \log \left (\frac {1}{3+x}\right )+21 x \log \left (\frac {1}{3+x}\right )+6 x^2 \log \left (\frac {1}{3+x}\right )\right )}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}\right ) \, dx\\ &=3 \int \frac {-10 \left (1-\frac {3 \log (2)}{5}\right )+6 \log \left (\frac {1}{3+x}\right )}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+9 \int \frac {x^2}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+9 \int \frac {e^{x+x^2} \left (6 x^3-29 x \left (1-\frac {21 \log (2)}{29}\right )-21 \left (1-\frac {3 \log (2)}{7}\right )+11 x^2 \left (1+\frac {6 \log (2)}{11}\right )+9 \log \left (\frac {1}{3+x}\right )+21 x \log \left (\frac {1}{3+x}\right )+6 x^2 \log \left (\frac {1}{3+x}\right )\right )}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+27 \int \frac {x}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+\int \frac {\left (5 \left (1-\frac {3 \log (2)}{5}\right )-3 \log \left (\frac {1}{3+x}\right )\right )^2}{x \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ &=3 \int \left (-\frac {6 x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {2}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )}\right ) \, dx+9 \int \frac {e^{x+x^2} \left (6 x^3-21 \left (1-\frac {3 \log (2)}{7}\right )+x (-29+21 \log (2))+x^2 (11+\log (64))+3 \left (3+7 x+2 x^2\right ) \log \left (\frac {1}{3+x}\right )\right )}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+9 \int \left (-\frac {3}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {9}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}\right ) \, dx+27 \int \left (\frac {1}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {3}{(-3-x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}\right ) \, dx+\int \left (\frac {1}{x}+\frac {6}{-3 x+5 \left (1-\frac {3 \log (2)}{5}\right )-3 \log \left (\frac {1}{3+x}\right )}+\frac {9 x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}\right ) \, dx\\ &=\log (x)+6 \int \frac {1}{-3 x+5 \left (1-\frac {3 \log (2)}{5}\right )-3 \log \left (\frac {1}{3+x}\right )} \, dx+6 \int \frac {1}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )} \, dx+2 \left (9 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\right )+9 \int \left (\frac {3 e^{x+x^2} (-2-x)}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {e^{x+x^2} (1+2 x)}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )}\right ) \, dx-18 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+81 \int \frac {1}{(-3-x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+81 \int \frac {1}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ &=\log (x)+6 \int \frac {1}{-3 x+5 \left (1-\frac {3 \log (2)}{5}\right )-3 \log \left (\frac {1}{3+x}\right )} \, dx+6 \int \frac {1}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )} \, dx+2 \left (9 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\right )+9 \int \frac {e^{x+x^2} (1+2 x)}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )} \, dx-18 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+27 \int \frac {e^{x+x^2} (-2-x)}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+81 \int \frac {1}{(-3-x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+81 \int \frac {1}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ &=\log (x)+6 \int \frac {1}{-3 x+5 \left (1-\frac {3 \log (2)}{5}\right )-3 \log \left (\frac {1}{3+x}\right )} \, dx+6 \int \frac {1}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )} \, dx+2 \left (9 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\right )+9 \int \left (\frac {e^{x+x^2}}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )}+\frac {2 e^{x+x^2} x}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )}\right ) \, dx-18 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+27 \int \left (-\frac {e^{x+x^2}}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}+\frac {e^{x+x^2}}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2}\right ) \, dx+81 \int \frac {1}{(-3-x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+81 \int \frac {1}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ &=\log (x)+6 \int \frac {1}{-3 x+5 \left (1-\frac {3 \log (2)}{5}\right )-3 \log \left (\frac {1}{3+x}\right )} \, dx+6 \int \frac {1}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )} \, dx+2 \left (9 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\right )+9 \int \frac {e^{x+x^2}}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )} \, dx-18 \int \frac {x}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+18 \int \frac {e^{x+x^2} x}{3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )} \, dx-27 \int \frac {e^{x+x^2}}{\left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+27 \int \frac {e^{x+x^2}}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+81 \int \frac {1}{(-3-x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx+81 \int \frac {1}{(3+x) \left (3 x-5 \left (1-\frac {3 \log (2)}{5}\right )+3 \log \left (\frac {1}{3+x}\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 31, normalized size = 1.03 \begin {gather*} \log (x)+\frac {9 e^{x+x^2}}{-5+3 x+3 \log (2)+3 \log \left (\frac {1}{3+x}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(3*x^2 + x^3 + E^(x + x^2)*(-6*x + 6*x^2 + 21*x^3 + 6*x^4) + (6*x + 2*x^2 + E^(x + x^2)*(9*x + 21*x^
2 + 6*x^3))*Log[2/(E^(5/3)*(3 + x))] + (3 + x)*Log[2/(E^(5/3)*(3 + x))]^2)/(3*x^3 + x^4 + (6*x^2 + 2*x^3)*Log[
2/(E^(5/3)*(3 + x))] + (3*x + x^2)*Log[2/(E^(5/3)*(3 + x))]^2),x]

[Out]

Log[x] + (9*E^(x + x^2))/(-5 + 3*x + 3*Log[2] + 3*Log[(3 + x)^(-1)])

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fricas [A]  time = 1.02, size = 39, normalized size = 1.30 \begin {gather*} \frac {{\left (x + \log \left (\frac {2 \, e^{\left (-\frac {5}{3}\right )}}{x + 3}\right )\right )} \log \relax (x) + 3 \, e^{\left (x^{2} + x\right )}}{x + \log \left (\frac {2 \, e^{\left (-\frac {5}{3}\right )}}{x + 3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3+x)*log(2/(3+x)/exp(5/3))^2+((6*x^3+21*x^2+9*x)*exp(x^2+x)+2*x^2+6*x)*log(2/(3+x)/exp(5/3))+(6*x^
4+21*x^3+6*x^2-6*x)*exp(x^2+x)+x^3+3*x^2)/((x^2+3*x)*log(2/(3+x)/exp(5/3))^2+(2*x^3+6*x^2)*log(2/(3+x)/exp(5/3
))+x^4+3*x^3),x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.57, size = 48, normalized size = 1.60 \begin {gather*} \frac {3 \, x \log \relax (x) + 3 \, \log \relax (x) \log \left (\frac {2}{x + 3}\right ) + 9 \, e^{\left (x^{2} + x\right )} - 5 \, \log \relax (x)}{3 \, x + 3 \, \log \left (\frac {2}{x + 3}\right ) - 5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3+x)*log(2/(3+x)/exp(5/3))^2+((6*x^3+21*x^2+9*x)*exp(x^2+x)+2*x^2+6*x)*log(2/(3+x)/exp(5/3))+(6*x^
4+21*x^3+6*x^2-6*x)*exp(x^2+x)+x^3+3*x^2)/((x^2+3*x)*log(2/(3+x)/exp(5/3))^2+(2*x^3+6*x^2)*log(2/(3+x)/exp(5/3
))+x^4+3*x^3),x, algorithm="giac")

[Out]

(3*x*log(x) + 3*log(x)*log(2/(x + 3)) + 9*e^(x^2 + x) - 5*log(x))/(3*x + 3*log(2/(x + 3)) - 5)

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maple [C]  time = 0.54, size = 34, normalized size = 1.13

method	result	size
risch	\(\ln \relax (x )+\frac {18 i {\mathrm e}^{\left (x +1\right ) x}}{6 i \ln \relax (2)+6 i x -6 i \ln \left (3+x \right )-10 i}\)	\(34\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3+x)*ln(2/(3+x)/exp(5/3))^2+((6*x^3+21*x^2+9*x)*exp(x^2+x)+2*x^2+6*x)*ln(2/(3+x)/exp(5/3))+(6*x^4+21*x^3
+6*x^2-6*x)*exp(x^2+x)+x^3+3*x^2)/((x^2+3*x)*ln(2/(3+x)/exp(5/3))^2+(2*x^3+6*x^2)*ln(2/(3+x)/exp(5/3))+x^4+3*x
^3),x,method=_RETURNVERBOSE)

[Out]

ln(x)+18*I*exp((x+1)*x)/(6*I*ln(2)+6*I*x-6*I*ln(3+x)-10*I)

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maxima [A]  time = 0.49, size = 28, normalized size = 0.93 \begin {gather*} \frac {9 \, e^{\left (x^{2} + x\right )}}{3 \, x + 3 \, \log \relax (2) - 3 \, \log \left (x + 3\right ) - 5} + \log \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3+x)*log(2/(3+x)/exp(5/3))^2+((6*x^3+21*x^2+9*x)*exp(x^2+x)+2*x^2+6*x)*log(2/(3+x)/exp(5/3))+(6*x^
4+21*x^3+6*x^2-6*x)*exp(x^2+x)+x^3+3*x^2)/((x^2+3*x)*log(2/(3+x)/exp(5/3))^2+(2*x^3+6*x^2)*log(2/(3+x)/exp(5/3
))+x^4+3*x^3),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 0.44, size = 41, normalized size = 1.37 \begin {gather*} \frac {3\,{\mathrm {e}}^{x^2+x}+\ln \left (\frac {2\,{\mathrm {e}}^{-\frac {5}{3}}}{x+3}\right )\,\ln \relax (x)+x\,\ln \relax (x)}{x+\ln \left (\frac {2\,{\mathrm {e}}^{-\frac {5}{3}}}{x+3}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log((2*exp(-5/3))/(x + 3))*(6*x + exp(x + x^2)*(9*x + 21*x^2 + 6*x^3) + 2*x^2) + exp(x + x^2)*(6*x^2 - 6*
x + 21*x^3 + 6*x^4) + 3*x^2 + x^3 + log((2*exp(-5/3))/(x + 3))^2*(x + 3))/(log((2*exp(-5/3))/(x + 3))^2*(3*x +
x^2) + log((2*exp(-5/3))/(x + 3))*(6*x^2 + 2*x^3) + 3*x^3 + x^4),x)

[Out]

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

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sympy [A]  time = 0.52, size = 24, normalized size = 0.80 \begin {gather*} \log {\relax (x )} + \frac {3 e^{x^{2} + x}}{x + \log {\left (\frac {2}{\left (x + 3\right ) e^{\frac {5}{3}}} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3+x)*ln(2/(3+x)/exp(5/3))**2+((6*x**3+21*x**2+9*x)*exp(x**2+x)+2*x**2+6*x)*ln(2/(3+x)/exp(5/3))+(6
*x**4+21*x**3+6*x**2-6*x)*exp(x**2+x)+x**3+3*x**2)/((x**2+3*x)*ln(2/(3+x)/exp(5/3))**2+(2*x**3+6*x**2)*ln(2/(3
+x)/exp(5/3))+x**4+3*x**3),x)

[Out]

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

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