3.42.34 \(\int \frac {e^{\frac {-15+3 x}{x+\log (x)}} (15 x^3+12 x^4+3 x^5+e^x (-15-12 x-x^3)+(-15 x^2-12 x^3-2 x^4) \log (15)+(9 x^4+e^x (-3 x-2 x^2)-7 x^3 \log (15)) \log (x)+(-e^x x+3 x^3-2 x^2 \log (15)) \log ^2(x))}{2 x^3+4 x^2 \log (x)+2 x \log ^2(x)} \, dx\)

Optimal. Leaf size=33 \[ \frac {1}{2} e^{\frac {3 (-5+x)}{x+\log (x)}} \left (-e^x+x^2 (x-\log (15))\right ) \]

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Rubi [F]  time = 15.94, 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 {e^{\frac {-15+3 x}{x+\log (x)}} \left (15 x^3+12 x^4+3 x^5+e^x \left (-15-12 x-x^3\right )+\left (-15 x^2-12 x^3-2 x^4\right ) \log (15)+\left (9 x^4+e^x \left (-3 x-2 x^2\right )-7 x^3 \log (15)\right ) \log (x)+\left (-e^x x+3 x^3-2 x^2 \log (15)\right ) \log ^2(x)\right )}{2 x^3+4 x^2 \log (x)+2 x \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-15 + 3*x)/(x + Log[x]))*(15*x^3 + 12*x^4 + 3*x^5 + E^x*(-15 - 12*x - x^3) + (-15*x^2 - 12*x^3 - 2*x^
4)*Log[15] + (9*x^4 + E^x*(-3*x - 2*x^2) - 7*x^3*Log[15])*Log[x] + (-(E^x*x) + 3*x^3 - 2*x^2*Log[15])*Log[x]^2
))/(2*x^3 + 4*x^2*Log[x] + 2*x*Log[x]^2),x]

[Out]

-1/2*Defer[Int][E^(x + (-15 + 3*x)/(x + Log[x])), x] - Log[15]*Defer[Int][E^((-15 + 3*x)/(x + Log[x]))*x, x] +
(3*Defer[Int][E^((-15 + 3*x)/(x + Log[x]))*x^2, x])/2 - 6*Defer[Int][E^(x + (-15 + 3*x)/(x + Log[x]))/(x + Lo
g[x])^2, x] - (15*Defer[Int][E^(x + (-15 + 3*x)/(x + Log[x]))/(x*(x + Log[x])^2), x])/2 - (15*Log[15]*Defer[In
t][(E^((-15 + 3*x)/(x + Log[x]))*x)/(x + Log[x])^2, x])/2 + (3*Defer[Int][(E^(x + (-15 + 3*x)/(x + Log[x]))*x)
/(x + Log[x])^2, x])/2 + (15*Defer[Int][(E^((-15 + 3*x)/(x + Log[x]))*x^2)/(x + Log[x])^2, x])/2 - 6*Log[15]*D
efer[Int][(E^((-15 + 3*x)/(x + Log[x]))*x^2)/(x + Log[x])^2, x] + 6*Defer[Int][(E^((-15 + 3*x)/(x + Log[x]))*x
^3)/(x + Log[x])^2, x] + (3*Log[15]*Defer[Int][(E^((-15 + 3*x)/(x + Log[x]))*x^3)/(x + Log[x])^2, x])/2 - (3*D
efer[Int][(E^((-15 + 3*x)/(x + Log[x]))*x^4)/(x + Log[x])^2, x])/2 - (3*Defer[Int][E^(x + (-15 + 3*x)/(x + Log
[x]))/(x + Log[x]), x])/2 - (3*Log[15]*Defer[Int][(E^((-15 + 3*x)/(x + Log[x]))*x^2)/(x + Log[x]), x])/2 + (3*
Defer[Int][(E^((-15 + 3*x)/(x + Log[x]))*x^3)/(x + Log[x]), x])/2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {-15+3 x}{x+\log (x)}} \left (15 x^3+12 x^4+3 x^5+e^x \left (-15-12 x-x^3\right )+\left (-15 x^2-12 x^3-2 x^4\right ) \log (15)+\left (9 x^4+e^x \left (-3 x-2 x^2\right )-7 x^3 \log (15)\right ) \log (x)+\left (-e^x x+3 x^3-2 x^2 \log (15)\right ) \log ^2(x)\right )}{2 x (x+\log (x))^2} \, dx\\ &=\frac {1}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} \left (15 x^3+12 x^4+3 x^5+e^x \left (-15-12 x-x^3\right )+\left (-15 x^2-12 x^3-2 x^4\right ) \log (15)+\left (9 x^4+e^x \left (-3 x-2 x^2\right )-7 x^3 \log (15)\right ) \log (x)+\left (-e^x x+3 x^3-2 x^2 \log (15)\right ) \log ^2(x)\right )}{x (x+\log (x))^2} \, dx\\ &=\frac {1}{2} \int \left (\frac {15 e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2}+\frac {12 e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2}+\frac {3 e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2}-\frac {e^{\frac {-15+3 x}{x+\log (x)}} x \left (15+12 x+2 x^2\right ) \log (15)}{(x+\log (x))^2}+\frac {9 e^{\frac {-15+3 x}{x+\log (x)}} x^3 \log (x)}{(x+\log (x))^2}-\frac {7 e^{\frac {-15+3 x}{x+\log (x)}} x^2 \log (15) \log (x)}{(x+\log (x))^2}+\frac {3 e^{\frac {-15+3 x}{x+\log (x)}} x^2 \log ^2(x)}{(x+\log (x))^2}-\frac {2 e^{\frac {-15+3 x}{x+\log (x)}} x \log (15) \log ^2(x)}{(x+\log (x))^2}-\frac {e^{x+\frac {-15+3 x}{x+\log (x)}} \left (15+12 x+x^3+3 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right )}{x (x+\log (x))^2}\right ) \, dx\\ &=-\left (\frac {1}{2} \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}} \left (15+12 x+x^3+3 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right )}{x (x+\log (x))^2} \, dx\right )+\frac {3}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx+\frac {3}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2 \log ^2(x)}{(x+\log (x))^2} \, dx+\frac {9}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3 \log (x)}{(x+\log (x))^2} \, dx+6 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx+\frac {15}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\frac {1}{2} \log (15) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x \left (15+12 x+2 x^2\right )}{(x+\log (x))^2} \, dx-\log (15) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x \log ^2(x)}{(x+\log (x))^2} \, dx-\frac {1}{2} (7 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2 \log (x)}{(x+\log (x))^2} \, dx\\ &=-\left (\frac {1}{2} \int \left (e^{x+\frac {-15+3 x}{x+\log (x)}}-\frac {3 e^{x+\frac {-15+3 x}{x+\log (x)}} \left (-5-4 x+x^2\right )}{x (x+\log (x))^2}+\frac {3 e^{x+\frac {-15+3 x}{x+\log (x)}}}{x+\log (x)}\right ) \, dx\right )+\frac {3}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx+\frac {3}{2} \int \left (e^{\frac {-15+3 x}{x+\log (x)}} x^2+\frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2}-\frac {2 e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)}\right ) \, dx+\frac {9}{2} \int \left (-\frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2}+\frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)}\right ) \, dx+6 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx+\frac {15}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\frac {1}{2} \log (15) \int \left (\frac {15 e^{\frac {-15+3 x}{x+\log (x)}} x}{(x+\log (x))^2}+\frac {12 e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2}+\frac {2 e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2}\right ) \, dx-\log (15) \int \left (e^{\frac {-15+3 x}{x+\log (x)}} x+\frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2}-\frac {2 e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)}\right ) \, dx-\frac {1}{2} (7 \log (15)) \int \left (-\frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2}+\frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)}\right ) \, dx\\ &=-\left (\frac {1}{2} \int e^{x+\frac {-15+3 x}{x+\log (x)}} \, dx\right )+\frac {3}{2} \int e^{\frac {-15+3 x}{x+\log (x)}} x^2 \, dx+2 \left (\frac {3}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx\right )+\frac {3}{2} \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}} \left (-5-4 x+x^2\right )}{x (x+\log (x))^2} \, dx-\frac {3}{2} \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}}}{x+\log (x)} \, dx-3 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)} \, dx-\frac {9}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx+\frac {9}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)} \, dx+6 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx+\frac {15}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\log (15) \int e^{\frac {-15+3 x}{x+\log (x)}} x \, dx-2 \left (\log (15) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx\right )+(2 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)} \, dx+\frac {1}{2} (7 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx-\frac {1}{2} (7 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)} \, dx-(6 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\frac {1}{2} (15 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x}{(x+\log (x))^2} \, dx\\ &=-\left (\frac {1}{2} \int e^{x+\frac {-15+3 x}{x+\log (x)}} \, dx\right )+\frac {3}{2} \int e^{\frac {-15+3 x}{x+\log (x)}} x^2 \, dx+2 \left (\frac {3}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx\right )-\frac {3}{2} \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}}}{x+\log (x)} \, dx+\frac {3}{2} \int \left (-\frac {4 e^{x+\frac {-15+3 x}{x+\log (x)}}}{(x+\log (x))^2}-\frac {5 e^{x+\frac {-15+3 x}{x+\log (x)}}}{x (x+\log (x))^2}+\frac {e^{x+\frac {-15+3 x}{x+\log (x)}} x}{(x+\log (x))^2}\right ) \, dx-3 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)} \, dx-\frac {9}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx+\frac {9}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)} \, dx+6 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx+\frac {15}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\log (15) \int e^{\frac {-15+3 x}{x+\log (x)}} x \, dx-2 \left (\log (15) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx\right )+(2 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)} \, dx+\frac {1}{2} (7 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx-\frac {1}{2} (7 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)} \, dx-(6 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\frac {1}{2} (15 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x}{(x+\log (x))^2} \, dx\\ &=-\left (\frac {1}{2} \int e^{x+\frac {-15+3 x}{x+\log (x)}} \, dx\right )+\frac {3}{2} \int e^{\frac {-15+3 x}{x+\log (x)}} x^2 \, dx+\frac {3}{2} \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}} x}{(x+\log (x))^2} \, dx+2 \left (\frac {3}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx\right )-\frac {3}{2} \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}}}{x+\log (x)} \, dx-3 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)} \, dx-\frac {9}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^4}{(x+\log (x))^2} \, dx+\frac {9}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{x+\log (x)} \, dx-6 \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}}}{(x+\log (x))^2} \, dx+6 \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx-\frac {15}{2} \int \frac {e^{x+\frac {-15+3 x}{x+\log (x)}}}{x (x+\log (x))^2} \, dx+\frac {15}{2} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\log (15) \int e^{\frac {-15+3 x}{x+\log (x)}} x \, dx-2 \left (\log (15) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx\right )+(2 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)} \, dx+\frac {1}{2} (7 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^3}{(x+\log (x))^2} \, dx-\frac {1}{2} (7 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{x+\log (x)} \, dx-(6 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x^2}{(x+\log (x))^2} \, dx-\frac {1}{2} (15 \log (15)) \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} x}{(x+\log (x))^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.65, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{\frac {-15+3 x}{x+\log (x)}} \left (15 x^3+12 x^4+3 x^5+e^x \left (-15-12 x-x^3\right )+\left (-15 x^2-12 x^3-2 x^4\right ) \log (15)+\left (9 x^4+e^x \left (-3 x-2 x^2\right )-7 x^3 \log (15)\right ) \log (x)+\left (-e^x x+3 x^3-2 x^2 \log (15)\right ) \log ^2(x)\right )}{2 x^3+4 x^2 \log (x)+2 x \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(E^((-15 + 3*x)/(x + Log[x]))*(15*x^3 + 12*x^4 + 3*x^5 + E^x*(-15 - 12*x - x^3) + (-15*x^2 - 12*x^3
- 2*x^4)*Log[15] + (9*x^4 + E^x*(-3*x - 2*x^2) - 7*x^3*Log[15])*Log[x] + (-(E^x*x) + 3*x^3 - 2*x^2*Log[15])*Lo
g[x]^2))/(2*x^3 + 4*x^2*Log[x] + 2*x*Log[x]^2),x]

[Out]

Integrate[(E^((-15 + 3*x)/(x + Log[x]))*(15*x^3 + 12*x^4 + 3*x^5 + E^x*(-15 - 12*x - x^3) + (-15*x^2 - 12*x^3
- 2*x^4)*Log[15] + (9*x^4 + E^x*(-3*x - 2*x^2) - 7*x^3*Log[15])*Log[x] + (-(E^x*x) + 3*x^3 - 2*x^2*Log[15])*Lo
g[x]^2))/(2*x^3 + 4*x^2*Log[x] + 2*x*Log[x]^2), x]

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fricas [A]  time = 0.72, size = 29, normalized size = 0.88 \begin {gather*} \frac {1}{2} \, {\left (x^{3} - x^{2} \log \left (15\right ) - e^{x}\right )} e^{\left (\frac {3 \, {\left (x - 5\right )}}{x + \log \relax (x)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(x)*x-2*x^2*log(15)+3*x^3)*log(x)^2+((-2*x^2-3*x)*exp(x)-7*x^3*log(15)+9*x^4)*log(x)+(-x^3-12*
x-15)*exp(x)+(-2*x^4-12*x^3-15*x^2)*log(15)+3*x^5+12*x^4+15*x^3)*exp((3*x-15)/(x+log(x)))/(2*x*log(x)^2+4*x^2*
log(x)+2*x^3),x, algorithm="fricas")

[Out]

1/2*(x^3 - x^2*log(15) - e^x)*e^(3*(x - 5)/(x + log(x)))

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giac [B]  time = 0.37, size = 59, normalized size = 1.79 \begin {gather*} \frac {1}{2} \, x^{3} e^{\left (\frac {3 \, {\left (x - 5\right )}}{x + \log \relax (x)}\right )} - \frac {1}{2} \, x^{2} e^{\left (\frac {3 \, {\left (x - 5\right )}}{x + \log \relax (x)}\right )} \log \left (15\right ) - \frac {1}{2} \, e^{\left (\frac {x^{2} + x \log \relax (x) + 3 \, x - 15}{x + \log \relax (x)}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(x)*x-2*x^2*log(15)+3*x^3)*log(x)^2+((-2*x^2-3*x)*exp(x)-7*x^3*log(15)+9*x^4)*log(x)+(-x^3-12*
x-15)*exp(x)+(-2*x^4-12*x^3-15*x^2)*log(15)+3*x^5+12*x^4+15*x^3)*exp((3*x-15)/(x+log(x)))/(2*x*log(x)^2+4*x^2*
log(x)+2*x^3),x, algorithm="giac")

[Out]

1/2*x^3*e^(3*(x - 5)/(x + log(x))) - 1/2*x^2*e^(3*(x - 5)/(x + log(x)))*log(15) - 1/2*e^((x^2 + x*log(x) + 3*x
- 15)/(x + log(x)))

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maple [A]  time = 0.08, size = 38, normalized size = 1.15

method	result	size
risch	\(\left (\frac {x^{3}}{2}-\frac {x^{2} \ln \relax (5)}{2}-\frac {x^{2} \ln \relax (3)}{2}-\frac {{\mathrm e}^{x}}{2}\right ) {\mathrm e}^{\frac {3 x -15}{x +\ln \relax (x )}}\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-exp(x)*x-2*x^2*ln(15)+3*x^3)*ln(x)^2+((-2*x^2-3*x)*exp(x)-7*x^3*ln(15)+9*x^4)*ln(x)+(-x^3-12*x-15)*exp(
x)+(-2*x^4-12*x^3-15*x^2)*ln(15)+3*x^5+12*x^4+15*x^3)*exp((3*x-15)/(x+ln(x)))/(2*x*ln(x)^2+4*x^2*ln(x)+2*x^3),
x,method=_RETURNVERBOSE)

[Out]

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

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(x)*x-2*x^2*log(15)+3*x^3)*log(x)^2+((-2*x^2-3*x)*exp(x)-7*x^3*log(15)+9*x^4)*log(x)+(-x^3-12*
x-15)*exp(x)+(-2*x^4-12*x^3-15*x^2)*log(15)+3*x^5+12*x^4+15*x^3)*exp((3*x-15)/(x+log(x)))/(2*x*log(x)^2+4*x^2*
log(x)+2*x^3),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [B]  time = 3.36, size = 56, normalized size = 1.70 \begin {gather*} \frac {x^3\,{\mathrm {e}}^{\frac {3\,x-15}{x+\ln \relax (x)}}}{2}-\frac {{\mathrm {e}}^{\frac {3\,x-15}{x+\ln \relax (x)}}\,{\mathrm {e}}^x}{2}-\frac {x^2\,{\mathrm {e}}^{\frac {3\,x-15}{x+\ln \relax (x)}}\,\ln \left (15\right )}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((3*x - 15)/(x + log(x)))*(log(x)*(7*x^3*log(15) + exp(x)*(3*x + 2*x^2) - 9*x^4) + exp(x)*(12*x + x^3
+ 15) + log(x)^2*(2*x^2*log(15) + x*exp(x) - 3*x^3) + log(15)*(15*x^2 + 12*x^3 + 2*x^4) - 15*x^3 - 12*x^4 - 3
*x^5))/(2*x*log(x)^2 + 4*x^2*log(x) + 2*x^3),x)

[Out]

(x^3*exp((3*x - 15)/(x + log(x))))/2 - (exp((3*x - 15)/(x + log(x)))*exp(x))/2 - (x^2*exp((3*x - 15)/(x + log(
x)))*log(15))/2

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sympy [A]  time = 39.02, size = 26, normalized size = 0.79 \begin {gather*} \frac {\left (x^{3} - x^{2} \log {\left (15 \right )} - e^{x}\right ) e^{\frac {3 x - 15}{x + \log {\relax (x )}}}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(x)*x-2*x**2*ln(15)+3*x**3)*ln(x)**2+((-2*x**2-3*x)*exp(x)-7*x**3*ln(15)+9*x**4)*ln(x)+(-x**3-
12*x-15)*exp(x)+(-2*x**4-12*x**3-15*x**2)*ln(15)+3*x**5+12*x**4+15*x**3)*exp((3*x-15)/(x+ln(x)))/(2*x*ln(x)**2
+4*x**2*ln(x)+2*x**3),x)

[Out]

(x**3 - x**2*log(15) - exp(x))*exp((3*x - 15)/(x + log(x)))/2

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