3.14.2 \(\int \frac {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} (-12-372 x-36 x^2)+e^{\frac {2}{5} (1+5 x)} (-360-3996 x-756 x^2-36 x^3)+e^{\frac {1}{5} (1+5 x)} (-3600-16320 x-4356 x^2-396 x^3-12 x^4)+(-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} (-36-756 x-72 x^2)+e^{\frac {1}{5} (1+5 x)} (-720-4392 x-792 x^2-36 x^3)) \log (x)+(-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} (-36-396 x-36 x^2)) \log ^2(x)+(-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x) \log ^3(x)}{x} \, dx\) [1302]

Optimal. Leaf size=26 \[ 1-x \left (1+\frac {3 \left (10+e^{\frac {1}{5}+x}+x+\log (x)\right )^4}{x}\right ) \]

[Out]

1-(1+3*(ln(x)+10+exp(1/5+x)+x)^4/x)*x

________________________________________________________________________________________

Rubi [F]
time = 1.94, 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 {-12000-15601 x-12 e^{\frac {4}{5} (1+5 x)} x-3960 x^2-372 x^3-12 x^4+e^{\frac {3}{5} (1+5 x)} \left (-12-372 x-36 x^2\right )+e^{\frac {2}{5} (1+5 x)} \left (-360-3996 x-756 x^2-36 x^3\right )+e^{\frac {1}{5} (1+5 x)} \left (-3600-16320 x-4356 x^2-396 x^3-12 x^4\right )+\left (-3600-4320 x-36 e^{\frac {3}{5} (1+5 x)} x-756 x^2-36 x^3+e^{\frac {2}{5} (1+5 x)} \left (-36-756 x-72 x^2\right )+e^{\frac {1}{5} (1+5 x)} \left (-720-4392 x-792 x^2-36 x^3\right )\right ) \log (x)+\left (-360-396 x-36 e^{\frac {2}{5} (1+5 x)} x-36 x^2+e^{\frac {1}{5} (1+5 x)} \left (-36-396 x-36 x^2\right )\right ) \log ^2(x)+\left (-12-12 x-12 e^{\frac {1}{5} (1+5 x)} x\right ) \log ^3(x)}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-12000 - 15601*x - 12*E^((4*(1 + 5*x))/5)*x - 3960*x^2 - 372*x^3 - 12*x^4 + E^((3*(1 + 5*x))/5)*(-12 - 37
2*x - 36*x^2) + E^((2*(1 + 5*x))/5)*(-360 - 3996*x - 756*x^2 - 36*x^3) + E^((1 + 5*x)/5)*(-3600 - 16320*x - 43
56*x^2 - 396*x^3 - 12*x^4) + (-3600 - 4320*x - 36*E^((3*(1 + 5*x))/5)*x - 756*x^2 - 36*x^3 + E^((2*(1 + 5*x))/
5)*(-36 - 756*x - 72*x^2) + E^((1 + 5*x)/5)*(-720 - 4392*x - 792*x^2 - 36*x^3))*Log[x] + (-360 - 396*x - 36*E^
((2*(1 + 5*x))/5)*x - 36*x^2 + E^((1 + 5*x)/5)*(-36 - 396*x - 36*x^2))*Log[x]^2 + (-12 - 12*x - 12*E^((1 + 5*x
)/5)*x)*Log[x]^3)/x,x]

[Out]

-12000*E^(1/5 + x) - 1800*E^(2/5 + 2*x) - 120*E^(3/5 + 3*x) - 3*E^(4/5 + 4*x) - 12001*x - 3600*E^(1/5 + x)*x -
360*E^(2/5 + 2*x)*x - 12*E^(3/5 + 3*x)*x - 1800*x^2 - 360*E^(1/5 + x)*x^2 - 18*E^(2/5 + 2*x)*x^2 - 120*x^3 -
12*E^(1/5 + x)*x^3 - 3*x^4 + 72*E^(1/5)*ExpIntegralEi[x] + 720*E^(1/5)*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2
}, x] + 72*E^(2/5)*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, 2*x] + 18*E^(2/5)*Log[-2*x]^2 + 360*E^(1/5)*Log[-
x]^2 - 12000*Log[x] - 3672*E^(1/5 + x)*Log[x] - 360*E^(2/5 + 2*x)*Log[x] - 12*E^(3/5 + 3*x)*Log[x] + 720*E^(1/
5)*EulerGamma*Log[x] + 36*E^(2/5)*EulerGamma*Log[x] - 3600*x*Log[x] - 720*E^(1/5 + x)*x*Log[x] - 36*E^(2/5 + 2
*x)*x*Log[x] - 360*x^2*Log[x] - 36*E^(1/5 + x)*x^2*Log[x] - 12*x^3*Log[x] - 720*E^(1/5)*ExpIntegralEi[x]*Log[x
] + 720*E^(1/5)*(ExpIntegralE[1, -x] + ExpIntegralEi[x])*Log[x] - 36*E^(2/5)*ExpIntegralEi[2*x]*Log[x] + 36*E^
(2/5)*(ExpIntegralE[1, -2*x] + ExpIntegralEi[2*x])*Log[x] - 1800*Log[x]^2 - 360*x*Log[x]^2 - 18*x^2*Log[x]^2 -
120*Log[x]^3 - 12*x*Log[x]^3 - 3*Log[x]^4 - 396*Defer[Int][E^(1/5 + x)*Log[x]^2, x] - 36*Defer[Int][E^(2/5 +
2*x)*Log[x]^2, x] - 36*Defer[Int][(E^(1/5 + x)*Log[x]^2)/x, x] - 36*Defer[Int][E^(1/5 + x)*x*Log[x]^2, x] - 12
*Defer[Int][E^(1/5 + x)*Log[x]^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-12 e^{\frac {4}{5}+4 x}-\frac {12 e^{\frac {1}{5}+x} (10+x+\log (x))^2 \left (3+13 x+x^2+x \log (x)\right )}{x}-\frac {12 e^{\frac {3}{5}+3 x} \left (1+31 x+3 x^2+3 x \log (x)\right )}{x}-\frac {36 e^{\frac {2}{5}+2 x} \left (10+111 x+21 x^2+x^3+\log (x)+21 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right )}{x}+\frac {-12000-15601 x-3960 x^2-372 x^3-12 x^4-3600 \log (x)-4320 x \log (x)-756 x^2 \log (x)-36 x^3 \log (x)-360 \log ^2(x)-396 x \log ^2(x)-36 x^2 \log ^2(x)-12 \log ^3(x)-12 x \log ^3(x)}{x}\right ) \, dx\\ &=-\left (12 \int e^{\frac {4}{5}+4 x} \, dx\right )-12 \int \frac {e^{\frac {1}{5}+x} (10+x+\log (x))^2 \left (3+13 x+x^2+x \log (x)\right )}{x} \, dx-12 \int \frac {e^{\frac {3}{5}+3 x} \left (1+31 x+3 x^2+3 x \log (x)\right )}{x} \, dx-36 \int \frac {e^{\frac {2}{5}+2 x} \left (10+111 x+21 x^2+x^3+\log (x)+21 x \log (x)+2 x^2 \log (x)+x \log ^2(x)\right )}{x} \, dx+\int \frac {-12000-15601 x-3960 x^2-372 x^3-12 x^4-3600 \log (x)-4320 x \log (x)-756 x^2 \log (x)-36 x^3 \log (x)-360 \log ^2(x)-396 x \log ^2(x)-36 x^2 \log ^2(x)-12 \log ^3(x)-12 x \log ^3(x)}{x} \, dx\\ &=-3 e^{\frac {4}{5}+4 x}-12 \int \left (\frac {e^{\frac {3}{5}+3 x} \left (1+31 x+3 x^2\right )}{x}+3 e^{\frac {3}{5}+3 x} \log (x)\right ) \, dx-12 \int \left (\frac {e^{\frac {1}{5}+x} (10+x)^2 \left (3+13 x+x^2\right )}{x}+\frac {3 e^{\frac {1}{5}+x} \left (20+122 x+22 x^2+x^3\right ) \log (x)}{x}+\frac {3 e^{\frac {1}{5}+x} \left (1+11 x+x^2\right ) \log ^2(x)}{x}+e^{\frac {1}{5}+x} \log ^3(x)\right ) \, dx-36 \int \left (\frac {e^{\frac {2}{5}+2 x} \left (10+111 x+21 x^2+x^3\right )}{x}+\frac {e^{\frac {2}{5}+2 x} \left (1+21 x+2 x^2\right ) \log (x)}{x}+e^{\frac {2}{5}+2 x} \log ^2(x)\right ) \, dx+\int \left (\frac {-12000-15601 x-3960 x^2-372 x^3-12 x^4}{x}-\frac {36 (1+x) (10+x)^2 \log (x)}{x}-\frac {36 \left (10+11 x+x^2\right ) \log ^2(x)}{x}-\frac {12 (1+x) \log ^3(x)}{x}\right ) \, dx\\ &=-3 e^{\frac {4}{5}+4 x}-12 \int \frac {e^{\frac {1}{5}+x} (10+x)^2 \left (3+13 x+x^2\right )}{x} \, dx-12 \int \frac {e^{\frac {3}{5}+3 x} \left (1+31 x+3 x^2\right )}{x} \, dx-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx-12 \int \frac {(1+x) \log ^3(x)}{x} \, dx-36 \int \frac {e^{\frac {2}{5}+2 x} \left (10+111 x+21 x^2+x^3\right )}{x} \, dx-36 \int e^{\frac {3}{5}+3 x} \log (x) \, dx-36 \int \frac {(1+x) (10+x)^2 \log (x)}{x} \, dx-36 \int \frac {e^{\frac {2}{5}+2 x} \left (1+21 x+2 x^2\right ) \log (x)}{x} \, dx-36 \int \frac {e^{\frac {1}{5}+x} \left (20+122 x+22 x^2+x^3\right ) \log (x)}{x} \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \frac {e^{\frac {1}{5}+x} \left (1+11 x+x^2\right ) \log ^2(x)}{x} \, dx-36 \int \frac {\left (10+11 x+x^2\right ) \log ^2(x)}{x} \, dx+\int \frac {-12000-15601 x-3960 x^2-372 x^3-12 x^4}{x} \, dx\\ &=-3 e^{\frac {4}{5}+4 x}-3672 e^{\frac {1}{5}+x} \log (x)-360 e^{\frac {2}{5}+2 x} \log (x)-12 e^{\frac {3}{5}+3 x} \log (x)-720 e^{\frac {1}{5}+x} x \log (x)-36 e^{\frac {2}{5}+2 x} x \log (x)-36 e^{\frac {1}{5}+x} x^2 \log (x)-720 \sqrt [5]{e} \text {Ei}(x) \log (x)-36 e^{2/5} \text {Ei}(2 x) \log (x)-12 \int \left (31 e^{\frac {3}{5}+3 x}+\frac {e^{\frac {3}{5}+3 x}}{x}+3 e^{\frac {3}{5}+3 x} x\right ) \, dx-12 \int \left (1360 e^{\frac {1}{5}+x}+\frac {300 e^{\frac {1}{5}+x}}{x}+363 e^{\frac {1}{5}+x} x+33 e^{\frac {1}{5}+x} x^2+e^{\frac {1}{5}+x} x^3\right ) \, dx-12 \int \log ^3(x) \, dx-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx-12 \int \frac {\log ^3(x)}{x} \, dx+36 \int \frac {e^{\frac {3}{5}+3 x}}{3 x} \, dx-36 \int \left (111 e^{\frac {2}{5}+2 x}+\frac {10 e^{\frac {2}{5}+2 x}}{x}+21 e^{\frac {2}{5}+2 x} x+e^{\frac {2}{5}+2 x} x^2\right ) \, dx+36 \int \frac {e^{\frac {1}{5}+x} \left (102+20 x+x^2\right )+20 \sqrt [5]{e} \text {Ei}(x)}{x} \, dx+36 \int \frac {e^{\frac {2}{5}+2 x} (10+x)+e^{2/5} \text {Ei}(2 x)}{x} \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \left (120 \log (x)+\frac {100 \log (x)}{x}+21 x \log (x)+x^2 \log (x)\right ) \, dx-36 \int \left (11 \log ^2(x)+\frac {10 \log ^2(x)}{x}+x \log ^2(x)\right ) \, dx-36 \int \left (11 e^{\frac {1}{5}+x} \log ^2(x)+\frac {e^{\frac {1}{5}+x} \log ^2(x)}{x}+e^{\frac {1}{5}+x} x \log ^2(x)\right ) \, dx+\int \left (-15601-\frac {12000}{x}-3960 x-372 x^2-12 x^3\right ) \, dx\\ &=-3 e^{\frac {4}{5}+4 x}-15601 x-1980 x^2-124 x^3-3 x^4-12000 \log (x)-3672 e^{\frac {1}{5}+x} \log (x)-360 e^{\frac {2}{5}+2 x} \log (x)-12 e^{\frac {3}{5}+3 x} \log (x)-720 e^{\frac {1}{5}+x} x \log (x)-36 e^{\frac {2}{5}+2 x} x \log (x)-36 e^{\frac {1}{5}+x} x^2 \log (x)-720 \sqrt [5]{e} \text {Ei}(x) \log (x)-36 e^{2/5} \text {Ei}(2 x) \log (x)-12 x \log ^3(x)-12 \int e^{\frac {1}{5}+x} x^3 \, dx-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx-12 \text {Subst}\left (\int x^3 \, dx,x,\log (x)\right )-36 \int e^{\frac {3}{5}+3 x} x \, dx-36 \int e^{\frac {2}{5}+2 x} x^2 \, dx+36 \int \left (\frac {e^{\frac {1}{5}+x} \left (102+20 x+x^2\right )}{x}+\frac {20 \sqrt [5]{e} \text {Ei}(x)}{x}\right ) \, dx+36 \int \left (\frac {e^{\frac {2}{5}+2 x} (10+x)}{x}+\frac {e^{2/5} \text {Ei}(2 x)}{x}\right ) \, dx-36 \int x^2 \log (x) \, dx+36 \int \log ^2(x) \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \frac {e^{\frac {1}{5}+x} \log ^2(x)}{x} \, dx-36 \int x \log ^2(x) \, dx-36 \int e^{\frac {1}{5}+x} x \log ^2(x) \, dx-360 \int \frac {e^{\frac {2}{5}+2 x}}{x} \, dx-360 \int \frac {\log ^2(x)}{x} \, dx-372 \int e^{\frac {3}{5}+3 x} \, dx-396 \int e^{\frac {1}{5}+x} x^2 \, dx-396 \int \log ^2(x) \, dx-396 \int e^{\frac {1}{5}+x} \log ^2(x) \, dx-756 \int e^{\frac {2}{5}+2 x} x \, dx-756 \int x \log (x) \, dx-3600 \int \frac {e^{\frac {1}{5}+x}}{x} \, dx-3600 \int \frac {\log (x)}{x} \, dx-3996 \int e^{\frac {2}{5}+2 x} \, dx-4320 \int \log (x) \, dx-4356 \int e^{\frac {1}{5}+x} x \, dx-16320 \int e^{\frac {1}{5}+x} \, dx\\ &=-16320 e^{\frac {1}{5}+x}-1998 e^{\frac {2}{5}+2 x}-124 e^{\frac {3}{5}+3 x}-3 e^{\frac {4}{5}+4 x}-11281 x-4356 e^{\frac {1}{5}+x} x-378 e^{\frac {2}{5}+2 x} x-12 e^{\frac {3}{5}+3 x} x-1791 x^2-396 e^{\frac {1}{5}+x} x^2-18 e^{\frac {2}{5}+2 x} x^2-120 x^3-12 e^{\frac {1}{5}+x} x^3-3 x^4-3600 \sqrt [5]{e} \text {Ei}(x)-360 e^{2/5} \text {Ei}(2 x)-12000 \log (x)-3672 e^{\frac {1}{5}+x} \log (x)-360 e^{\frac {2}{5}+2 x} \log (x)-12 e^{\frac {3}{5}+3 x} \log (x)-4320 x \log (x)-720 e^{\frac {1}{5}+x} x \log (x)-36 e^{\frac {2}{5}+2 x} x \log (x)-378 x^2 \log (x)-36 e^{\frac {1}{5}+x} x^2 \log (x)-12 x^3 \log (x)-720 \sqrt [5]{e} \text {Ei}(x) \log (x)-36 e^{2/5} \text {Ei}(2 x) \log (x)-1800 \log ^2(x)-360 x \log ^2(x)-18 x^2 \log ^2(x)-12 x \log ^3(x)-3 \log ^4(x)+12 \int e^{\frac {3}{5}+3 x} \, dx-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx+36 \int e^{\frac {2}{5}+2 x} x \, dx+36 \int e^{\frac {1}{5}+x} x^2 \, dx+36 \int \frac {e^{\frac {2}{5}+2 x} (10+x)}{x} \, dx+36 \int \frac {e^{\frac {1}{5}+x} \left (102+20 x+x^2\right )}{x} \, dx+36 \int x \log (x) \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \frac {e^{\frac {1}{5}+x} \log ^2(x)}{x} \, dx-36 \int e^{\frac {1}{5}+x} x \log ^2(x) \, dx-72 \int \log (x) \, dx-360 \text {Subst}\left (\int x^2 \, dx,x,\log (x)\right )+378 \int e^{\frac {2}{5}+2 x} \, dx-396 \int e^{\frac {1}{5}+x} \log ^2(x) \, dx+792 \int e^{\frac {1}{5}+x} x \, dx+792 \int \log (x) \, dx+4356 \int e^{\frac {1}{5}+x} \, dx+\left (720 \sqrt [5]{e}\right ) \int \frac {\text {Ei}(x)}{x} \, dx+\left (36 e^{2/5}\right ) \int \frac {\text {Ei}(2 x)}{x} \, dx\\ &=-11964 e^{\frac {1}{5}+x}-1809 e^{\frac {2}{5}+2 x}-120 e^{\frac {3}{5}+3 x}-3 e^{\frac {4}{5}+4 x}-12001 x-3564 e^{\frac {1}{5}+x} x-360 e^{\frac {2}{5}+2 x} x-12 e^{\frac {3}{5}+3 x} x-1800 x^2-360 e^{\frac {1}{5}+x} x^2-18 e^{\frac {2}{5}+2 x} x^2-120 x^3-12 e^{\frac {1}{5}+x} x^3-3 x^4-3600 \sqrt [5]{e} \text {Ei}(x)-360 e^{2/5} \text {Ei}(2 x)-12000 \log (x)-3672 e^{\frac {1}{5}+x} \log (x)-360 e^{\frac {2}{5}+2 x} \log (x)-12 e^{\frac {3}{5}+3 x} \log (x)-3600 x \log (x)-720 e^{\frac {1}{5}+x} x \log (x)-36 e^{\frac {2}{5}+2 x} x \log (x)-360 x^2 \log (x)-36 e^{\frac {1}{5}+x} x^2 \log (x)-12 x^3 \log (x)-720 \sqrt [5]{e} \text {Ei}(x) \log (x)+720 \sqrt [5]{e} (E_1(-x)+\text {Ei}(x)) \log (x)-36 e^{2/5} \text {Ei}(2 x) \log (x)+36 e^{2/5} (E_1(-2 x)+\text {Ei}(2 x)) \log (x)-1800 \log ^2(x)-360 x \log ^2(x)-18 x^2 \log ^2(x)-120 \log ^3(x)-12 x \log ^3(x)-3 \log ^4(x)-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx-18 \int e^{\frac {2}{5}+2 x} \, dx+36 \int \left (e^{\frac {2}{5}+2 x}+\frac {10 e^{\frac {2}{5}+2 x}}{x}\right ) \, dx+36 \int \left (20 e^{\frac {1}{5}+x}+\frac {102 e^{\frac {1}{5}+x}}{x}+e^{\frac {1}{5}+x} x\right ) \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \frac {e^{\frac {1}{5}+x} \log ^2(x)}{x} \, dx-36 \int e^{\frac {1}{5}+x} x \log ^2(x) \, dx-72 \int e^{\frac {1}{5}+x} x \, dx-396 \int e^{\frac {1}{5}+x} \log ^2(x) \, dx-792 \int e^{\frac {1}{5}+x} \, dx-\left (720 \sqrt [5]{e}\right ) \int \frac {E_1(-x)}{x} \, dx-\left (36 e^{2/5}\right ) \int \frac {E_1(-2 x)}{x} \, dx\\ &=-12756 e^{\frac {1}{5}+x}-1818 e^{\frac {2}{5}+2 x}-120 e^{\frac {3}{5}+3 x}-3 e^{\frac {4}{5}+4 x}-12001 x-3636 e^{\frac {1}{5}+x} x-360 e^{\frac {2}{5}+2 x} x-12 e^{\frac {3}{5}+3 x} x-1800 x^2-360 e^{\frac {1}{5}+x} x^2-18 e^{\frac {2}{5}+2 x} x^2-120 x^3-12 e^{\frac {1}{5}+x} x^3-3 x^4-3600 \sqrt [5]{e} \text {Ei}(x)-360 e^{2/5} \text {Ei}(2 x)+720 \sqrt [5]{e} x \, _3F_3(1,1,1;2,2,2;x)+72 e^{2/5} x \, _3F_3(1,1,1;2,2,2;2 x)+18 e^{2/5} \log ^2(-2 x)+360 \sqrt [5]{e} \log ^2(-x)-12000 \log (x)-3672 e^{\frac {1}{5}+x} \log (x)-360 e^{\frac {2}{5}+2 x} \log (x)-12 e^{\frac {3}{5}+3 x} \log (x)+720 \sqrt [5]{e} \gamma \log (x)+36 e^{2/5} \gamma \log (x)-3600 x \log (x)-720 e^{\frac {1}{5}+x} x \log (x)-36 e^{\frac {2}{5}+2 x} x \log (x)-360 x^2 \log (x)-36 e^{\frac {1}{5}+x} x^2 \log (x)-12 x^3 \log (x)-720 \sqrt [5]{e} \text {Ei}(x) \log (x)+720 \sqrt [5]{e} (E_1(-x)+\text {Ei}(x)) \log (x)-36 e^{2/5} \text {Ei}(2 x) \log (x)+36 e^{2/5} (E_1(-2 x)+\text {Ei}(2 x)) \log (x)-1800 \log ^2(x)-360 x \log ^2(x)-18 x^2 \log ^2(x)-120 \log ^3(x)-12 x \log ^3(x)-3 \log ^4(x)-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx+36 \int e^{\frac {2}{5}+2 x} \, dx+36 \int e^{\frac {1}{5}+x} x \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \frac {e^{\frac {1}{5}+x} \log ^2(x)}{x} \, dx-36 \int e^{\frac {1}{5}+x} x \log ^2(x) \, dx+72 \int e^{\frac {1}{5}+x} \, dx+360 \int \frac {e^{\frac {2}{5}+2 x}}{x} \, dx-396 \int e^{\frac {1}{5}+x} \log ^2(x) \, dx+720 \int e^{\frac {1}{5}+x} \, dx+3672 \int \frac {e^{\frac {1}{5}+x}}{x} \, dx\\ &=-11964 e^{\frac {1}{5}+x}-1800 e^{\frac {2}{5}+2 x}-120 e^{\frac {3}{5}+3 x}-3 e^{\frac {4}{5}+4 x}-12001 x-3600 e^{\frac {1}{5}+x} x-360 e^{\frac {2}{5}+2 x} x-12 e^{\frac {3}{5}+3 x} x-1800 x^2-360 e^{\frac {1}{5}+x} x^2-18 e^{\frac {2}{5}+2 x} x^2-120 x^3-12 e^{\frac {1}{5}+x} x^3-3 x^4+72 \sqrt [5]{e} \text {Ei}(x)+720 \sqrt [5]{e} x \, _3F_3(1,1,1;2,2,2;x)+72 e^{2/5} x \, _3F_3(1,1,1;2,2,2;2 x)+18 e^{2/5} \log ^2(-2 x)+360 \sqrt [5]{e} \log ^2(-x)-12000 \log (x)-3672 e^{\frac {1}{5}+x} \log (x)-360 e^{\frac {2}{5}+2 x} \log (x)-12 e^{\frac {3}{5}+3 x} \log (x)+720 \sqrt [5]{e} \gamma \log (x)+36 e^{2/5} \gamma \log (x)-3600 x \log (x)-720 e^{\frac {1}{5}+x} x \log (x)-36 e^{\frac {2}{5}+2 x} x \log (x)-360 x^2 \log (x)-36 e^{\frac {1}{5}+x} x^2 \log (x)-12 x^3 \log (x)-720 \sqrt [5]{e} \text {Ei}(x) \log (x)+720 \sqrt [5]{e} (E_1(-x)+\text {Ei}(x)) \log (x)-36 e^{2/5} \text {Ei}(2 x) \log (x)+36 e^{2/5} (E_1(-2 x)+\text {Ei}(2 x)) \log (x)-1800 \log ^2(x)-360 x \log ^2(x)-18 x^2 \log ^2(x)-120 \log ^3(x)-12 x \log ^3(x)-3 \log ^4(x)-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx-36 \int e^{\frac {1}{5}+x} \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \frac {e^{\frac {1}{5}+x} \log ^2(x)}{x} \, dx-36 \int e^{\frac {1}{5}+x} x \log ^2(x) \, dx-396 \int e^{\frac {1}{5}+x} \log ^2(x) \, dx\\ &=-12000 e^{\frac {1}{5}+x}-1800 e^{\frac {2}{5}+2 x}-120 e^{\frac {3}{5}+3 x}-3 e^{\frac {4}{5}+4 x}-12001 x-3600 e^{\frac {1}{5}+x} x-360 e^{\frac {2}{5}+2 x} x-12 e^{\frac {3}{5}+3 x} x-1800 x^2-360 e^{\frac {1}{5}+x} x^2-18 e^{\frac {2}{5}+2 x} x^2-120 x^3-12 e^{\frac {1}{5}+x} x^3-3 x^4+72 \sqrt [5]{e} \text {Ei}(x)+720 \sqrt [5]{e} x \, _3F_3(1,1,1;2,2,2;x)+72 e^{2/5} x \, _3F_3(1,1,1;2,2,2;2 x)+18 e^{2/5} \log ^2(-2 x)+360 \sqrt [5]{e} \log ^2(-x)-12000 \log (x)-3672 e^{\frac {1}{5}+x} \log (x)-360 e^{\frac {2}{5}+2 x} \log (x)-12 e^{\frac {3}{5}+3 x} \log (x)+720 \sqrt [5]{e} \gamma \log (x)+36 e^{2/5} \gamma \log (x)-3600 x \log (x)-720 e^{\frac {1}{5}+x} x \log (x)-36 e^{\frac {2}{5}+2 x} x \log (x)-360 x^2 \log (x)-36 e^{\frac {1}{5}+x} x^2 \log (x)-12 x^3 \log (x)-720 \sqrt [5]{e} \text {Ei}(x) \log (x)+720 \sqrt [5]{e} (E_1(-x)+\text {Ei}(x)) \log (x)-36 e^{2/5} \text {Ei}(2 x) \log (x)+36 e^{2/5} (E_1(-2 x)+\text {Ei}(2 x)) \log (x)-1800 \log ^2(x)-360 x \log ^2(x)-18 x^2 \log ^2(x)-120 \log ^3(x)-12 x \log ^3(x)-3 \log ^4(x)-12 \int e^{\frac {1}{5}+x} \log ^3(x) \, dx-36 \int e^{\frac {2}{5}+2 x} \log ^2(x) \, dx-36 \int \frac {e^{\frac {1}{5}+x} \log ^2(x)}{x} \, dx-36 \int e^{\frac {1}{5}+x} x \log ^2(x) \, dx-396 \int e^{\frac {1}{5}+x} \log ^2(x) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(130\) vs. \(2(26)=52\).
time = 0.20, size = 130, normalized size = 5.00 \begin {gather*} -3 e^{\frac {4}{5}+4 x}-12 e^{\frac {3}{5}+3 x} (10+x)-18 e^{\frac {2}{5}+2 x} (10+x)^2-12 e^{\frac {1}{5}+x} (10+x)^3-x \left (12001+1800 x+120 x^2+3 x^3\right )-12 \left (10+e^{\frac {1}{5}+x}+x\right )^3 \log (x)-18 \left (10+e^{\frac {1}{5}+x}+x\right )^2 \log ^2(x)-12 \left (10+e^{\frac {1}{5}+x}+x\right ) \log ^3(x)-3 \log ^4(x) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-12000 - 15601*x - 12*E^((4*(1 + 5*x))/5)*x - 3960*x^2 - 372*x^3 - 12*x^4 + E^((3*(1 + 5*x))/5)*(-1
2 - 372*x - 36*x^2) + E^((2*(1 + 5*x))/5)*(-360 - 3996*x - 756*x^2 - 36*x^3) + E^((1 + 5*x)/5)*(-3600 - 16320*
x - 4356*x^2 - 396*x^3 - 12*x^4) + (-3600 - 4320*x - 36*E^((3*(1 + 5*x))/5)*x - 756*x^2 - 36*x^3 + E^((2*(1 +
5*x))/5)*(-36 - 756*x - 72*x^2) + E^((1 + 5*x)/5)*(-720 - 4392*x - 792*x^2 - 36*x^3))*Log[x] + (-360 - 396*x -
36*E^((2*(1 + 5*x))/5)*x - 36*x^2 + E^((1 + 5*x)/5)*(-36 - 396*x - 36*x^2))*Log[x]^2 + (-12 - 12*x - 12*E^((1
+ 5*x)/5)*x)*Log[x]^3)/x,x]

[Out]

-3*E^(4/5 + 4*x) - 12*E^(3/5 + 3*x)*(10 + x) - 18*E^(2/5 + 2*x)*(10 + x)^2 - 12*E^(1/5 + x)*(10 + x)^3 - x*(12
001 + 1800*x + 120*x^2 + 3*x^3) - 12*(10 + E^(1/5 + x) + x)^3*Log[x] - 18*(10 + E^(1/5 + x) + x)^2*Log[x]^2 -
12*(10 + E^(1/5 + x) + x)*Log[x]^3 - 3*Log[x]^4

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(226\) vs. \(2(23)=46\).
time = 0.12, size = 227, normalized size = 8.73

method	result	size
risch	\(-3 \ln \left (x \right )^{4}+\left (-12 x -12 \,{\mathrm e}^{\frac {1}{5}+x}-120\right ) \ln \left (x \right )^{3}+\left (-18 x^{2}-36 x \,{\mathrm e}^{\frac {1}{5}+x}-18 \,{\mathrm e}^{\frac {2}{5}+2 x}-360 x -360 \,{\mathrm e}^{\frac {1}{5}+x}-1800\right ) \ln \left (x \right )^{2}+\left (-12 x^{3}-36 \,{\mathrm e}^{\frac {1}{5}+x} x^{2}-36 x \,{\mathrm e}^{\frac {2}{5}+2 x}-12 \,{\mathrm e}^{\frac {3}{5}+3 x}-360 x^{2}-720 x \,{\mathrm e}^{\frac {1}{5}+x}-360 \,{\mathrm e}^{\frac {2}{5}+2 x}-3600 x -3600 \,{\mathrm e}^{\frac {1}{5}+x}-12000\right ) \ln \left (x \right )-3 x^{4}-12 \,{\mathrm e}^{\frac {1}{5}+x} x^{3}-18 \,{\mathrm e}^{\frac {2}{5}+2 x} x^{2}-12 x \,{\mathrm e}^{\frac {3}{5}+3 x}-3 \,{\mathrm e}^{\frac {4}{5}+4 x}-120 x^{3}-360 \,{\mathrm e}^{\frac {1}{5}+x} x^{2}-360 x \,{\mathrm e}^{\frac {2}{5}+2 x}-120 \,{\mathrm e}^{\frac {3}{5}+3 x}-1800 x^{2}-3600 x \,{\mathrm e}^{\frac {1}{5}+x}-1800 \,{\mathrm e}^{\frac {2}{5}+2 x}-12001 x -12000 \,{\mathrm e}^{\frac {1}{5}+x}\)	\(227\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-12*x*exp(1/5+x)-12*x-12)*ln(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^2-396*x-36)*exp(1/5+x)-36*x^2-396*x-360)*ln
(x)^2+(-36*x*exp(1/5+x)^3+(-72*x^2-756*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x^3-756*x
^2-4320*x-3600)*ln(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+x)^3+(-36*x^3-756*x^2-3996*x-360)*exp(1/5+x
)^2+(-12*x^4-396*x^3-4356*x^2-16320*x-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x,method=_RETU
RNVERBOSE)

[Out]

-3*ln(x)^4+(-12*x-12*exp(1/5+x)-120)*ln(x)^3+(-18*x^2-36*x*exp(1/5+x)-18*exp(2/5+2*x)-360*x-360*exp(1/5+x)-180
0)*ln(x)^2+(-12*x^3-36*exp(1/5+x)*x^2-36*x*exp(2/5+2*x)-12*exp(3/5+3*x)-360*x^2-720*x*exp(1/5+x)-360*exp(2/5+2
*x)-3600*x-3600*exp(1/5+x)-12000)*ln(x)-3*x^4-12*exp(1/5+x)*x^3-18*exp(2/5+2*x)*x^2-12*x*exp(3/5+3*x)-3*exp(4/
5+4*x)-120*x^3-360*exp(1/5+x)*x^2-360*x*exp(2/5+2*x)-120*exp(3/5+3*x)-1800*x^2-3600*x*exp(1/5+x)-1800*exp(2/5+
2*x)-12001*x-12000*exp(1/5+x)

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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x*exp(1/5+x)-12*x-12)*log(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^2-396*x-36)*exp(1/5+x)-36*x^2-396*x-
360)*log(x)^2+(-36*x*exp(1/5+x)^3+(-72*x^2-756*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x
^3-756*x^2-4320*x-3600)*log(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+x)^3+(-36*x^3-756*x^2-3996*x-360)*
exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-16320*x-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x, al
gorithm="maxima")

[Out]

-3*x^4 - 12*x^3*log(x) - 12*(x + 10)*log(x)^3 - 3*log(x)^4 - 120*x^3 - 378*x^2*log(x) - 18*(x^2 + 20*x)*log(x)
^2 - 1800*x^2 - 12*Ei(3*x)*e^(3/5) - 360*Ei(2*x)*e^(2/5) + 792*Ei(x)*e^(1/5) - 4*(3*x*e^(3/5) - e^(3/5))*e^(3*
x) - 9*(2*x^2*e^(2/5) - 2*x*e^(2/5) + e^(2/5))*e^(2*x) - 18*(e^(2/5)*log(x)^2 + 2*(x*e^(2/5) + 10*e^(2/5))*log
(x))*e^(2*x) - 189*(2*x*e^(2/5) - e^(2/5))*e^(2*x) - 12*(x^3*e^(1/5) - 3*x^2*e^(1/5) + 6*x*e^(1/5) - 6*e^(1/5)
)*e^x - 12*(e^(1/5)*log(x)^3 + 3*(x*e^(1/5) + 10*e^(1/5))*log(x)^2 + 3*(x^2*e^(1/5) + 20*x*e^(1/5) - 22*e^(1/5
))*log(x))*e^x - 396*(x^2*e^(1/5) - 2*x*e^(1/5) + 2*e^(1/5))*e^x - 4356*(x*e^(1/5) - e^(1/5))*e^x + 18*(x^2 +
40*x)*log(x) - 4320*x*log(x) - 12*e^(3*x + 3/5)*log(x) - 4392*e^(x + 1/5)*log(x) - 1800*log(x)^2 - 12001*x - 3
*e^(4*x + 4/5) - 124*e^(3*x + 3/5) - 1998*e^(2*x + 2/5) - 16320*e^(x + 1/5) + integrate(36*(x*e^(2/5) + 10*e^(
2/5))*e^(2*x)/x, x) + integrate(36*(x^2*e^(1/5) + 20*x*e^(1/5) - 22*e^(1/5))*e^x/x, x) + 12*integrate(e^(3*x +
3/5)/x, x) - 12000*log(x)

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 169 vs. \(2 (23) = 46\).
time = 0.36, size = 169, normalized size = 6.50 \begin {gather*} -3 \, x^{4} - 12 \, {\left (x + e^{\left (x + \frac {1}{5}\right )} + 10\right )} \log \left (x\right )^{3} - 3 \, \log \left (x\right )^{4} - 120 \, x^{3} - 18 \, {\left (x^{2} + 2 \, {\left (x + 10\right )} e^{\left (x + \frac {1}{5}\right )} + 20 \, x + e^{\left (2 \, x + \frac {2}{5}\right )} + 100\right )} \log \left (x\right )^{2} - 1800 \, x^{2} - 12 \, {\left (x + 10\right )} e^{\left (3 \, x + \frac {3}{5}\right )} - 18 \, {\left (x^{2} + 20 \, x + 100\right )} e^{\left (2 \, x + \frac {2}{5}\right )} - 12 \, {\left (x^{3} + 30 \, x^{2} + 300 \, x + 1000\right )} e^{\left (x + \frac {1}{5}\right )} - 12 \, {\left (x^{3} + 30 \, x^{2} + 3 \, {\left (x + 10\right )} e^{\left (2 \, x + \frac {2}{5}\right )} + 3 \, {\left (x^{2} + 20 \, x + 100\right )} e^{\left (x + \frac {1}{5}\right )} + 300 \, x + e^{\left (3 \, x + \frac {3}{5}\right )} + 1000\right )} \log \left (x\right ) - 12001 \, x - 3 \, e^{\left (4 \, x + \frac {4}{5}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x*exp(1/5+x)-12*x-12)*log(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^2-396*x-36)*exp(1/5+x)-36*x^2-396*x-
360)*log(x)^2+(-36*x*exp(1/5+x)^3+(-72*x^2-756*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x
^3-756*x^2-4320*x-3600)*log(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+x)^3+(-36*x^3-756*x^2-3996*x-360)*
exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-16320*x-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x, al
gorithm="fricas")

[Out]

-3*x^4 - 12*(x + e^(x + 1/5) + 10)*log(x)^3 - 3*log(x)^4 - 120*x^3 - 18*(x^2 + 2*(x + 10)*e^(x + 1/5) + 20*x +
e^(2*x + 2/5) + 100)*log(x)^2 - 1800*x^2 - 12*(x + 10)*e^(3*x + 3/5) - 18*(x^2 + 20*x + 100)*e^(2*x + 2/5) -
12*(x^3 + 30*x^2 + 300*x + 1000)*e^(x + 1/5) - 12*(x^3 + 30*x^2 + 3*(x + 10)*e^(2*x + 2/5) + 3*(x^2 + 20*x + 1
00)*e^(x + 1/5) + 300*x + e^(3*x + 3/5) + 1000)*log(x) - 12001*x - 3*e^(4*x + 4/5)

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 212 vs. \(2 (22) = 44\).
time = 0.40, size = 212, normalized size = 8.15 \begin {gather*} - 3 x^{4} - 120 x^{3} - 1800 x^{2} - 12001 x + \left (- 12 x - 120\right ) \log {\left (x \right )}^{3} + \left (- 12 x - 12 \log {\left (x \right )} - 120\right ) e^{3 x + \frac {3}{5}} + \left (- 18 x^{2} - 360 x - 1800\right ) \log {\left (x \right )}^{2} + \left (- 12 x^{3} - 360 x^{2} - 3600 x\right ) \log {\left (x \right )} + \left (- 18 x^{2} - 36 x \log {\left (x \right )} - 360 x - 18 \log {\left (x \right )}^{2} - 360 \log {\left (x \right )} - 1800\right ) e^{2 x + \frac {2}{5}} + \left (- 12 x^{3} - 36 x^{2} \log {\left (x \right )} - 360 x^{2} - 36 x \log {\left (x \right )}^{2} - 720 x \log {\left (x \right )} - 3600 x - 12 \log {\left (x \right )}^{3} - 360 \log {\left (x \right )}^{2} - 3600 \log {\left (x \right )} - 12000\right ) e^{x + \frac {1}{5}} - 3 e^{4 x + \frac {4}{5}} - 3 \log {\left (x \right )}^{4} - 12000 \log {\left (x \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x*exp(1/5+x)-12*x-12)*ln(x)**3+(-36*x*exp(1/5+x)**2+(-36*x**2-396*x-36)*exp(1/5+x)-36*x**2-396
*x-360)*ln(x)**2+(-36*x*exp(1/5+x)**3+(-72*x**2-756*x-36)*exp(1/5+x)**2+(-36*x**3-792*x**2-4392*x-720)*exp(1/5
+x)-36*x**3-756*x**2-4320*x-3600)*ln(x)-12*x*exp(1/5+x)**4+(-36*x**2-372*x-12)*exp(1/5+x)**3+(-36*x**3-756*x**
2-3996*x-360)*exp(1/5+x)**2+(-12*x**4-396*x**3-4356*x**2-16320*x-3600)*exp(1/5+x)-12*x**4-372*x**3-3960*x**2-1
5601*x-12000)/x,x)

[Out]

-3*x**4 - 120*x**3 - 1800*x**2 - 12001*x + (-12*x - 120)*log(x)**3 + (-12*x - 12*log(x) - 120)*exp(3*x + 3/5)
+ (-18*x**2 - 360*x - 1800)*log(x)**2 + (-12*x**3 - 360*x**2 - 3600*x)*log(x) + (-18*x**2 - 36*x*log(x) - 360*
x - 18*log(x)**2 - 360*log(x) - 1800)*exp(2*x + 2/5) + (-12*x**3 - 36*x**2*log(x) - 360*x**2 - 36*x*log(x)**2
- 720*x*log(x) - 3600*x - 12*log(x)**3 - 360*log(x)**2 - 3600*log(x) - 12000)*exp(x + 1/5) - 3*exp(4*x + 4/5)
- 3*log(x)**4 - 12000*log(x)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 759 vs. \(2 (23) = 46\).
time = 0.46, size = 759, normalized size = 29.19 \begin {gather*} -\frac {3}{625} \, {\left (5 \, x + 1\right )}^{4} - \frac {12}{125} \, {\left (5 \, x + 1\right )}^{3} e^{\left (x + \frac {1}{5}\right )} + \frac {12}{125} \, {\left (5 \, x + 1\right )}^{3} \log \left (5\right ) + \frac {36}{25} \, {\left (5 \, x + 1\right )}^{2} e^{\left (x + \frac {1}{5}\right )} \log \left (5\right ) - \frac {18}{25} \, {\left (5 \, x + 1\right )}^{2} \log \left (5\right )^{2} - \frac {36}{5} \, {\left (5 \, x + 1\right )} e^{\left (x + \frac {1}{5}\right )} \log \left (5\right )^{2} + \frac {12}{5} \, {\left (5 \, x + 1\right )} \log \left (5\right )^{3} + 12 \, e^{\left (x + \frac {1}{5}\right )} \log \left (5\right )^{3} - \frac {12}{125} \, {\left (5 \, x + 1\right )}^{3} \log \left (5 \, x\right ) - \frac {36}{25} \, {\left (5 \, x + 1\right )}^{2} e^{\left (x + \frac {1}{5}\right )} \log \left (5 \, x\right ) + \frac {36}{25} \, {\left (5 \, x + 1\right )}^{2} \log \left (5\right ) \log \left (5 \, x\right ) + \frac {72}{5} \, {\left (5 \, x + 1\right )} e^{\left (x + \frac {1}{5}\right )} \log \left (5\right ) \log \left (5 \, x\right ) - \frac {36}{5} \, {\left (5 \, x + 1\right )} \log \left (5\right )^{2} \log \left (5 \, x\right ) - 36 \, e^{\left (x + \frac {1}{5}\right )} \log \left (5\right )^{2} \log \left (5 \, x\right ) + 12 \, \log \left (5\right )^{3} \log \left (5 \, x\right ) - \frac {18}{25} \, {\left (5 \, x + 1\right )}^{2} \log \left (5 \, x\right )^{2} - \frac {36}{5} \, {\left (5 \, x + 1\right )} e^{\left (x + \frac {1}{5}\right )} \log \left (5 \, x\right )^{2} + \frac {36}{5} \, {\left (5 \, x + 1\right )} \log \left (5\right ) \log \left (5 \, x\right )^{2} + 36 \, e^{\left (x + \frac {1}{5}\right )} \log \left (5\right ) \log \left (5 \, x\right )^{2} - 18 \, \log \left (5\right )^{2} \log \left (5 \, x\right )^{2} - \frac {12}{5} \, {\left (5 \, x + 1\right )} \log \left (5 \, x\right )^{3} - 12 \, e^{\left (x + \frac {1}{5}\right )} \log \left (5 \, x\right )^{3} + 12 \, \log \left (5\right ) \log \left (5 \, x\right )^{3} - 3 \, \log \left (5 \, x\right )^{4} - \frac {588}{625} \, {\left (5 \, x + 1\right )}^{3} - \frac {18}{25} \, {\left (5 \, x + 1\right )}^{2} e^{\left (2 \, x + \frac {2}{5}\right )} - \frac {1764}{125} \, {\left (5 \, x + 1\right )}^{2} e^{\left (x + \frac {1}{5}\right )} + \frac {1764}{125} \, {\left (5 \, x + 1\right )}^{2} \log \left (5\right ) + \frac {36}{5} \, {\left (5 \, x + 1\right )} e^{\left (2 \, x + \frac {2}{5}\right )} \log \left (5\right ) + \frac {3528}{25} \, {\left (5 \, x + 1\right )} e^{\left (x + \frac {1}{5}\right )} \log \left (5\right ) - \frac {1764}{25} \, {\left (5 \, x + 1\right )} \log \left (5\right )^{2} - 18 \, e^{\left (2 \, x + \frac {2}{5}\right )} \log \left (5\right )^{2} - \frac {1764}{5} \, e^{\left (x + \frac {1}{5}\right )} \log \left (5\right )^{2} - \frac {1764}{125} \, {\left (5 \, x + 1\right )}^{2} \log \left (5 \, x\right ) - \frac {36}{5} \, {\left (5 \, x + 1\right )} e^{\left (2 \, x + \frac {2}{5}\right )} \log \left (5 \, x\right ) - \frac {3528}{25} \, {\left (5 \, x + 1\right )} e^{\left (x + \frac {1}{5}\right )} \log \left (5 \, x\right ) + \frac {3528}{25} \, {\left (5 \, x + 1\right )} \log \left (5\right ) \log \left (5 \, x\right ) + 36 \, e^{\left (2 \, x + \frac {2}{5}\right )} \log \left (5\right ) \log \left (5 \, x\right ) + \frac {3528}{5} \, e^{\left (x + \frac {1}{5}\right )} \log \left (5\right ) \log \left (5 \, x\right ) - \frac {1764}{5} \, \log \left (5\right )^{2} \log \left (5 \, x\right ) - \frac {1764}{25} \, {\left (5 \, x + 1\right )} \log \left (5 \, x\right )^{2} - 18 \, e^{\left (2 \, x + \frac {2}{5}\right )} \log \left (5 \, x\right )^{2} - \frac {1764}{5} \, e^{\left (x + \frac {1}{5}\right )} \log \left (5 \, x\right )^{2} + \frac {1764}{5} \, \log \left (5\right ) \log \left (5 \, x\right )^{2} - \frac {588}{5} \, \log \left (5 \, x\right )^{3} - \frac {43218}{625} \, {\left (5 \, x + 1\right )}^{2} - \frac {12}{5} \, {\left (5 \, x + 1\right )} e^{\left (3 \, x + \frac {3}{5}\right )} - \frac {1764}{25} \, {\left (5 \, x + 1\right )} e^{\left (2 \, x + \frac {2}{5}\right )} - \frac {86436}{125} \, {\left (5 \, x + 1\right )} e^{\left (x + \frac {1}{5}\right )} + \frac {86436}{125} \, {\left (5 \, x + 1\right )} \log \left (5\right ) + 12 \, e^{\left (3 \, x + \frac {3}{5}\right )} \log \left (5\right ) + \frac {1764}{5} \, e^{\left (2 \, x + \frac {2}{5}\right )} \log \left (5\right ) + \frac {86436}{25} \, e^{\left (x + \frac {1}{5}\right )} \log \left (5\right ) - \frac {86436}{125} \, {\left (5 \, x + 1\right )} \log \left (5 \, x\right ) - 12 \, e^{\left (3 \, x + \frac {3}{5}\right )} \log \left (5 \, x\right ) - \frac {1764}{5} \, e^{\left (2 \, x + \frac {2}{5}\right )} \log \left (5 \, x\right ) - \frac {86436}{25} \, e^{\left (x + \frac {1}{5}\right )} \log \left (5 \, x\right ) + \frac {86436}{25} \, \log \left (5\right ) \log \left (5 \, x\right ) - \frac {43218}{25} \, \log \left (5 \, x\right )^{2} - \frac {1411913}{125} \, x - 3 \, e^{\left (4 \, x + \frac {4}{5}\right )} - \frac {588}{5} \, e^{\left (3 \, x + \frac {3}{5}\right )} - \frac {43218}{25} \, e^{\left (2 \, x + \frac {2}{5}\right )} - \frac {1411788}{125} \, e^{\left (x + \frac {1}{5}\right )} - \frac {1411788}{125} \, \log \left (5 \, x\right ) - \frac {1411913}{625} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-12*x*exp(1/5+x)-12*x-12)*log(x)^3+(-36*x*exp(1/5+x)^2+(-36*x^2-396*x-36)*exp(1/5+x)-36*x^2-396*x-
360)*log(x)^2+(-36*x*exp(1/5+x)^3+(-72*x^2-756*x-36)*exp(1/5+x)^2+(-36*x^3-792*x^2-4392*x-720)*exp(1/5+x)-36*x
^3-756*x^2-4320*x-3600)*log(x)-12*x*exp(1/5+x)^4+(-36*x^2-372*x-12)*exp(1/5+x)^3+(-36*x^3-756*x^2-3996*x-360)*
exp(1/5+x)^2+(-12*x^4-396*x^3-4356*x^2-16320*x-3600)*exp(1/5+x)-12*x^4-372*x^3-3960*x^2-15601*x-12000)/x,x, al
gorithm="giac")

[Out]

-3/625*(5*x + 1)^4 - 12/125*(5*x + 1)^3*e^(x + 1/5) + 12/125*(5*x + 1)^3*log(5) + 36/25*(5*x + 1)^2*e^(x + 1/5
)*log(5) - 18/25*(5*x + 1)^2*log(5)^2 - 36/5*(5*x + 1)*e^(x + 1/5)*log(5)^2 + 12/5*(5*x + 1)*log(5)^3 + 12*e^(
x + 1/5)*log(5)^3 - 12/125*(5*x + 1)^3*log(5*x) - 36/25*(5*x + 1)^2*e^(x + 1/5)*log(5*x) + 36/25*(5*x + 1)^2*l
og(5)*log(5*x) + 72/5*(5*x + 1)*e^(x + 1/5)*log(5)*log(5*x) - 36/5*(5*x + 1)*log(5)^2*log(5*x) - 36*e^(x + 1/5
)*log(5)^2*log(5*x) + 12*log(5)^3*log(5*x) - 18/25*(5*x + 1)^2*log(5*x)^2 - 36/5*(5*x + 1)*e^(x + 1/5)*log(5*x
)^2 + 36/5*(5*x + 1)*log(5)*log(5*x)^2 + 36*e^(x + 1/5)*log(5)*log(5*x)^2 - 18*log(5)^2*log(5*x)^2 - 12/5*(5*x
+ 1)*log(5*x)^3 - 12*e^(x + 1/5)*log(5*x)^3 + 12*log(5)*log(5*x)^3 - 3*log(5*x)^4 - 588/625*(5*x + 1)^3 - 18/
25*(5*x + 1)^2*e^(2*x + 2/5) - 1764/125*(5*x + 1)^2*e^(x + 1/5) + 1764/125*(5*x + 1)^2*log(5) + 36/5*(5*x + 1)
*e^(2*x + 2/5)*log(5) + 3528/25*(5*x + 1)*e^(x + 1/5)*log(5) - 1764/25*(5*x + 1)*log(5)^2 - 18*e^(2*x + 2/5)*l
og(5)^2 - 1764/5*e^(x + 1/5)*log(5)^2 - 1764/125*(5*x + 1)^2*log(5*x) - 36/5*(5*x + 1)*e^(2*x + 2/5)*log(5*x)
- 3528/25*(5*x + 1)*e^(x + 1/5)*log(5*x) + 3528/25*(5*x + 1)*log(5)*log(5*x) + 36*e^(2*x + 2/5)*log(5)*log(5*x
) + 3528/5*e^(x + 1/5)*log(5)*log(5*x) - 1764/5*log(5)^2*log(5*x) - 1764/25*(5*x + 1)*log(5*x)^2 - 18*e^(2*x +
2/5)*log(5*x)^2 - 1764/5*e^(x + 1/5)*log(5*x)^2 + 1764/5*log(5)*log(5*x)^2 - 588/5*log(5*x)^3 - 43218/625*(5*
x + 1)^2 - 12/5*(5*x + 1)*e^(3*x + 3/5) - 1764/25*(5*x + 1)*e^(2*x + 2/5) - 86436/125*(5*x + 1)*e^(x + 1/5) +
86436/125*(5*x + 1)*log(5) + 12*e^(3*x + 3/5)*log(5) + 1764/5*e^(2*x + 2/5)*log(5) + 86436/25*e^(x + 1/5)*log(
5) - 86436/125*(5*x + 1)*log(5*x) - 12*e^(3*x + 3/5)*log(5*x) - 1764/5*e^(2*x + 2/5)*log(5*x) - 86436/25*e^(x
+ 1/5)*log(5*x) + 86436/25*log(5)*log(5*x) - 43218/25*log(5*x)^2 - 1411913/125*x - 3*e^(4*x + 4/5) - 588/5*e^(
3*x + 3/5) - 43218/25*e^(2*x + 2/5) - 1411788/125*e^(x + 1/5) - 1411788/125*log(5*x) - 1411913/625

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Mupad [B]
time = 3.77, size = 269, normalized size = 10.35 \begin {gather*} -12001\,x-12000\,{\mathrm {e}}^{x+\frac {1}{5}}-1800\,{\mathrm {e}}^{2\,x+\frac {2}{5}}-120\,{\mathrm {e}}^{3\,x+\frac {3}{5}}-3\,{\mathrm {e}}^{4\,x+\frac {4}{5}}-12000\,\ln \left (x\right )-3600\,x\,{\mathrm {e}}^{x+\frac {1}{5}}-360\,x\,{\ln \left (x\right )}^2-360\,x^2\,\ln \left (x\right )-12\,x\,{\ln \left (x\right )}^3-12\,x^3\,\ln \left (x\right )-18\,{\mathrm {e}}^{2\,x+\frac {2}{5}}\,{\ln \left (x\right )}^2-1800\,{\ln \left (x\right )}^2-120\,{\ln \left (x\right )}^3-3\,{\ln \left (x\right )}^4-360\,x\,{\mathrm {e}}^{2\,x+\frac {2}{5}}-12\,x\,{\mathrm {e}}^{3\,x+\frac {3}{5}}-360\,x^2\,{\mathrm {e}}^{x+\frac {1}{5}}-12\,x^3\,{\mathrm {e}}^{x+\frac {1}{5}}-18\,x^2\,{\ln \left (x\right )}^2-3600\,{\mathrm {e}}^{x+\frac {1}{5}}\,\ln \left (x\right )-3600\,x\,\ln \left (x\right )-18\,x^2\,{\mathrm {e}}^{2\,x+\frac {2}{5}}-1800\,x^2-120\,x^3-3\,x^4-360\,{\mathrm {e}}^{2\,x+\frac {2}{5}}\,\ln \left (x\right )-12\,{\mathrm {e}}^{3\,x+\frac {3}{5}}\,\ln \left (x\right )-360\,{\mathrm {e}}^{x+\frac {1}{5}}\,{\ln \left (x\right )}^2-12\,{\mathrm {e}}^{x+\frac {1}{5}}\,{\ln \left (x\right )}^3-36\,x\,{\mathrm {e}}^{2\,x+\frac {2}{5}}\,\ln \left (x\right )-36\,x\,{\mathrm {e}}^{x+\frac {1}{5}}\,{\ln \left (x\right )}^2-36\,x^2\,{\mathrm {e}}^{x+\frac {1}{5}}\,\ln \left (x\right )-720\,x\,{\mathrm {e}}^{x+\frac {1}{5}}\,\ln \left (x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(15601*x + log(x)*(4320*x + exp(x + 1/5)*(4392*x + 792*x^2 + 36*x^3 + 720) + exp(2*x + 2/5)*(756*x + 72*x
^2 + 36) + 36*x*exp(3*x + 3/5) + 756*x^2 + 36*x^3 + 3600) + exp(3*x + 3/5)*(372*x + 36*x^2 + 12) + 12*x*exp(4*
x + 4/5) + exp(x + 1/5)*(16320*x + 4356*x^2 + 396*x^3 + 12*x^4 + 3600) + log(x)^2*(396*x + exp(x + 1/5)*(396*x
+ 36*x^2 + 36) + 36*x*exp(2*x + 2/5) + 36*x^2 + 360) + exp(2*x + 2/5)*(3996*x + 756*x^2 + 36*x^3 + 360) + 396
0*x^2 + 372*x^3 + 12*x^4 + log(x)^3*(12*x + 12*x*exp(x + 1/5) + 12) + 12000)/x,x)

[Out]

- 12001*x - 12000*exp(x + 1/5) - 1800*exp(2*x + 2/5) - 120*exp(3*x + 3/5) - 3*exp(4*x + 4/5) - 12000*log(x) -
3600*x*exp(x + 1/5) - 360*x*log(x)^2 - 360*x^2*log(x) - 12*x*log(x)^3 - 12*x^3*log(x) - 18*exp(2*x + 2/5)*log(
x)^2 - 1800*log(x)^2 - 120*log(x)^3 - 3*log(x)^4 - 360*x*exp(2*x + 2/5) - 12*x*exp(3*x + 3/5) - 360*x^2*exp(x
+ 1/5) - 12*x^3*exp(x + 1/5) - 18*x^2*log(x)^2 - 3600*exp(x + 1/5)*log(x) - 3600*x*log(x) - 18*x^2*exp(2*x + 2
/5) - 1800*x^2 - 120*x^3 - 3*x^4 - 360*exp(2*x + 2/5)*log(x) - 12*exp(3*x + 3/5)*log(x) - 360*exp(x + 1/5)*log
(x)^2 - 12*exp(x + 1/5)*log(x)^3 - 36*x*exp(2*x + 2/5)*log(x) - 36*x*exp(x + 1/5)*log(x)^2 - 36*x^2*exp(x + 1/
5)*log(x) - 720*x*exp(x + 1/5)*log(x)

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