3.25.85 \(\int \frac {(\frac {3+3 x}{x})^{\frac {e^{e^4 x} (5-x)}{x}} ((2 x+2 x^2) \log (\frac {3+3 x}{x})+e^{e^4 x} \log (\frac {3+3 x}{x}) (-10+2 x+(-10-10 x+e^4 (10 x+8 x^2-2 x^3)) \log (\frac {3+3 x}{x})))}{(x+x^2) \log (\frac {3+3 x}{x})} \, dx\)

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

________________________________________________________________________________________

Rubi [F]  time = 10.99, 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 {\left (\frac {3+3 x}{x}\right )^{\frac {e^{e^4 x} (5-x)}{x}} \left (\left (2 x+2 x^2\right ) \log \left (\frac {3+3 x}{x}\right )+e^{e^4 x} \log \left (\frac {3+3 x}{x}\right ) \left (-10+2 x+\left (-10-10 x+e^4 \left (10 x+8 x^2-2 x^3\right )\right ) \log \left (\frac {3+3 x}{x}\right )\right )\right )}{\left (x+x^2\right ) \log \left (\frac {3+3 x}{x}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(((3 + 3*x)/x)^((E^(E^4*x)*(5 - x))/x)*((2*x + 2*x^2)*Log[(3 + 3*x)/x] + E^(E^4*x)*Log[(3 + 3*x)/x]*(-10 +
2*x + (-10 - 10*x + E^4*(10*x + 8*x^2 - 2*x^3))*Log[(3 + 3*x)/x])))/((x + x^2)*Log[(3 + 3*x)/x]),x]

[Out]

2*Defer[Int][(3 + 3/x)^(-((E^(E^4*x)*(-5 + x))/x)), x] + 10*Log[3 + 3/x]*Defer[Int][E^(4 + E^4*x)/(3 + 3/x)^((
E^(E^4*x)*(-5 + x))/x), x] - 10*Defer[Int][E^(E^4*x)/((3 + 3/x)^((E^(E^4*x)*(-5 + x))/x)*x), x] - 10*Log[3 + 3
/x]*Defer[Int][E^(E^4*x)/((3 + 3/x)^((E^(E^4*x)*(-5 + x))/x)*x), x] - 2*Log[3 + 3/x]*Defer[Int][(E^(4 + E^4*x)
*x)/(3 + 3/x)^((E^(E^4*x)*(-5 + x))/x), x] + 12*Defer[Int][E^(E^4*x)/((3 + 3/x)^((E^(E^4*x)*(-5 + x))/x)*(1 +
x)), x] + 10*Defer[Int][Defer[Int][E^(4 + E^4*x)/(3 + 3/x)^((E^(E^4*x)*(-5 + x))/x), x]/x, x] - 10*Defer[Int][
Defer[Int][E^(4 + E^4*x)/(3 + 3/x)^((E^(E^4*x)*(-5 + x))/x), x]/(1 + x), x] - 10*Defer[Int][Defer[Int][E^(E^4*
x)/((3 + 3/x)^((E^(E^4*x)*(-5 + x))/x)*x), x]/x, x] + 10*Defer[Int][Defer[Int][E^(E^4*x)/((3 + 3/x)^((E^(E^4*x
)*(-5 + x))/x)*x), x]/(1 + x), x] - 2*Defer[Int][Defer[Int][(E^(4 + E^4*x)*x)/(3 + 3/x)^((E^(E^4*x)*(-5 + x))/
x), x]/x, x] + 2*Defer[Int][Defer[Int][(E^(4 + E^4*x)*x)/(3 + 3/x)^((E^(E^4*x)*(-5 + x))/x), x]/(1 + x), x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]  time = 0.16, size = 26, normalized size = 0.90 \begin {gather*} 2 \left (3+\frac {3}{x}\right )^{-\frac {e^{e^4 x} (-5+x)}{x}} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(((3 + 3*x)/x)^((E^(E^4*x)*(5 - x))/x)*((2*x + 2*x^2)*Log[(3 + 3*x)/x] + E^(E^4*x)*Log[(3 + 3*x)/x]*
(-10 + 2*x + (-10 - 10*x + E^4*(10*x + 8*x^2 - 2*x^3))*Log[(3 + 3*x)/x])))/((x + x^2)*Log[(3 + 3*x)/x]),x]

[Out]

(2*x)/(3 + 3/x)^((E^(E^4*x)*(-5 + x))/x)

________________________________________________________________________________________

fricas [A]  time = 0.79, size = 28, normalized size = 0.97 \begin {gather*} 2 \, x e^{\left (-\frac {{\left (x - 5\right )} e^{\left (x e^{4} + \log \left (\log \left (\frac {3 \, {\left (x + 1\right )}}{x}\right )\right )\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*x^3+8*x^2+10*x)*exp(4)-10*x-10)*log((3*x+3)/x)+2*x-10)*exp(log(log((3*x+3)/x))+x*exp(4))+(2*x
^2+2*x)*log((3*x+3)/x))*exp((5-x)*exp(log(log((3*x+3)/x))+x*exp(4))/x)/(x^2+x)/log((3*x+3)/x),x, algorithm="fr
icas")

[Out]

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

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*x^3+8*x^2+10*x)*exp(4)-10*x-10)*log((3*x+3)/x)+2*x-10)*exp(log(log((3*x+3)/x))+x*exp(4))+(2*x
^2+2*x)*log((3*x+3)/x))*exp((5-x)*exp(log(log((3*x+3)/x))+x*exp(4))/x)/(x^2+x)/log((3*x+3)/x),x, algorithm="gi
ac")

[Out]

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

________________________________________________________________________________________

maple [F]  time = 0.18, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (\left (\left (-2 x^{3}+8 x^{2}+10 x \right ) {\mathrm e}^{4}-10 x -10\right ) \ln \left (\frac {3 x +3}{x}\right )+2 x -10\right ) {\mathrm e}^{\ln \left (\ln \left (\frac {3 x +3}{x}\right )\right )+x \,{\mathrm e}^{4}}+\left (2 x^{2}+2 x \right ) \ln \left (\frac {3 x +3}{x}\right )\right ) {\mathrm e}^{\frac {\left (5-x \right ) {\mathrm e}^{\ln \left (\ln \left (\frac {3 x +3}{x}\right )\right )+x \,{\mathrm e}^{4}}}{x}}}{\left (x^{2}+x \right ) \ln \left (\frac {3 x +3}{x}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-2*x^3+8*x^2+10*x)*exp(4)-10*x-10)*ln((3*x+3)/x)+2*x-10)*exp(ln(ln((3*x+3)/x))+x*exp(4))+(2*x^2+2*x)*l
n((3*x+3)/x))*exp((5-x)*exp(ln(ln((3*x+3)/x))+x*exp(4))/x)/(x^2+x)/ln((3*x+3)/x),x)

[Out]

int(((((-2*x^3+8*x^2+10*x)*exp(4)-10*x-10)*ln((3*x+3)/x)+2*x-10)*exp(ln(ln((3*x+3)/x))+x*exp(4))+(2*x^2+2*x)*l
n((3*x+3)/x))*exp((5-x)*exp(ln(ln((3*x+3)/x))+x*exp(4))/x)/(x^2+x)/ln((3*x+3)/x),x)

________________________________________________________________________________________

maxima [B]  time = 0.91, size = 71, normalized size = 2.45 \begin {gather*} 2 \, x e^{\left (-e^{\left (x e^{4}\right )} \log \relax (3) - e^{\left (x e^{4}\right )} \log \left (x + 1\right ) + e^{\left (x e^{4}\right )} \log \relax (x) + \frac {5 \, e^{\left (x e^{4}\right )} \log \relax (3)}{x} + \frac {5 \, e^{\left (x e^{4}\right )} \log \left (x + 1\right )}{x} - \frac {5 \, e^{\left (x e^{4}\right )} \log \relax (x)}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-2*x^3+8*x^2+10*x)*exp(4)-10*x-10)*log((3*x+3)/x)+2*x-10)*exp(log(log((3*x+3)/x))+x*exp(4))+(2*x
^2+2*x)*log((3*x+3)/x))*exp((5-x)*exp(log(log((3*x+3)/x))+x*exp(4))/x)/(x^2+x)/log((3*x+3)/x),x, algorithm="ma
xima")

[Out]

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

________________________________________________________________________________________

mupad [B]  time = 1.93, size = 29, normalized size = 1.00 \begin {gather*} 2\,x\,{\left (\frac {3}{x}+3\right )}^{\frac {5\,{\mathrm {e}}^{x\,{\mathrm {e}}^4}}{x}-{\mathrm {e}}^{x\,{\mathrm {e}}^4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

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(((((-2*x**3+8*x**2+10*x)*exp(4)-10*x-10)*ln((3*x+3)/x)+2*x-10)*exp(ln(ln((3*x+3)/x))+x*exp(4))+(2*x*
*2+2*x)*ln((3*x+3)/x))*exp((5-x)*exp(ln(ln((3*x+3)/x))+x*exp(4))/x)/(x**2+x)/ln((3*x+3)/x),x)

[Out]

Timed out

________________________________________________________________________________________