3.42.38 \(\int \frac {e^{\frac {-5 e^{-1+x}-14 x-5 x^2+e^x (e^{-1+x}+3 x+x^2)+(5-e^x) \log (x^2)}{x}} (10+e^{-1+x} (5-5 x)-5 x^2+e^x (-2+4 x^2+x^3+e^{-1+x} (-1+2 x))+(-5+e^x (1-x)) \log (x^2))}{x^2} \, dx\)

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

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Rubi [F]  time = 32.52, 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 {\exp \left (\frac {-5 e^{-1+x}-14 x-5 x^2+e^x \left (e^{-1+x}+3 x+x^2\right )+\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (10+e^{-1+x} (5-5 x)-5 x^2+e^x \left (-2+4 x^2+x^3+e^{-1+x} (-1+2 x)\right )+\left (-5+e^x (1-x)\right ) \log \left (x^2\right )\right )}{x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-5*E^(-1 + x) - 14*x - 5*x^2 + E^x*(E^(-1 + x) + 3*x + x^2) + (5 - E^x)*Log[x^2])/x)*(10 + E^(-1 + x)
*(5 - 5*x) - 5*x^2 + E^x*(-2 + 4*x^2 + x^3 + E^(-1 + x)*(-1 + 2*x)) + (-5 + E^x*(1 - x))*Log[x^2]))/x^2,x]

[Out]

-5*Defer[Int][E^(-14 - (5*E^(-1 + x))/x - 5*x + (E^x*(E^(-1 + x) + 3*x + x^2))/x + ((5 - E^x)*Log[x^2])/x), x]
+ 4*Defer[Int][E^(-14 - (5*E^(-1 + x))/x - 4*x + (E^x*(E^(-1 + x) + 3*x + x^2))/x + ((5 - E^x)*Log[x^2])/x),
x] + 10*Defer[Int][E^(-14 - (5*E^(-1 + x))/x - 5*x + (E^x*(E^(-1 + x) + 3*x + x^2))/x + ((5 - E^x)*Log[x^2])/x
)/x^2, x] + (5 - 2*E)*Defer[Int][E^(-15 - (5*E^(-1 + x))/x - 4*x + (E^x*(E^(-1 + x) + 3*x + x^2))/x + ((5 - E^
x)*Log[x^2])/x)/x^2, x] - Defer[Int][E^(-15 - (5*E^(-1 + x))/x - 3*x + (E^x*(E^(-1 + x) + 3*x + x^2))/x + ((5
- E^x)*Log[x^2])/x)/x^2, x] - 5*Defer[Int][E^(-15 - (5*E^(-1 + x))/x - 4*x + (E^x*(E^(-1 + x) + 3*x + x^2))/x
+ ((5 - E^x)*Log[x^2])/x)/x, x] + 2*Defer[Int][E^(-15 - (5*E^(-1 + x))/x - 3*x + (E^x*(E^(-1 + x) + 3*x + x^2)
)/x + ((5 - E^x)*Log[x^2])/x)/x, x] + Defer[Int][E^(-14 - (5*E^(-1 + x))/x - 4*x + (E^x*(E^(-1 + x) + 3*x + x^
2))/x + ((5 - E^x)*Log[x^2])/x)*x, x] - 5*Defer[Int][(E^(-14 - (5*E^(-1 + x))/x - 5*x + (E^x*(E^(-1 + x) + 3*x
+ x^2))/x + ((5 - E^x)*Log[x^2])/x)*Log[x^2])/x^2, x] + Defer[Int][(E^(-14 - (5*E^(-1 + x))/x - 4*x + (E^x*(E
^(-1 + x) + 3*x + x^2))/x + ((5 - E^x)*Log[x^2])/x)*Log[x^2])/x^2, x] - Defer[Int][(E^(-14 - (5*E^(-1 + x))/x
- 4*x + (E^x*(E^(-1 + x) + 3*x + x^2))/x + ((5 - E^x)*Log[x^2])/x)*Log[x^2])/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (10+e^{-1+x} (5-5 x)-5 x^2+e^x \left (-2+4 x^2+x^3+e^{-1+x} (-1+2 x)\right )+\left (-5+e^x (1-x)\right ) \log \left (x^2\right )\right )}{x^2} \, dx\\ &=\int \left (\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+2 x)}{x^2}-\frac {5 \exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2+\log \left (x^2\right )\right )}{x^2}+\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5 \left (1-\frac {2 e}{5}\right )-5 x+4 e x^2+e x^3+e \log \left (x^2\right )-e x \log \left (x^2\right )\right )}{x^2}\right ) \, dx\\ &=-\left (5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2+\log \left (x^2\right )\right )}{x^2} \, dx\right )+\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+2 x)}{x^2} \, dx+\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5 \left (1-\frac {2 e}{5}\right )-5 x+4 e x^2+e x^3+e \log \left (x^2\right )-e x \log \left (x^2\right )\right )}{x^2} \, dx\\ &=-\left (5 \int \left (\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2\right )}{x^2}+\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2}\right ) \, dx\right )+\int \left (-\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2}+\frac {2 \exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x}\right ) \, dx+\int \left (\frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5-2 e-5 x+4 e x^2+e x^3\right )}{x^2}-\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+x) \log \left (x^2\right )}{x^2}\right ) \, dx\\ &=2 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (-2+x^2\right )}{x^2} \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx-\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \left (5-2 e-5 x+4 e x^2+e x^3\right )}{x^2} \, dx-\int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) (-1+x) \log \left (x^2\right )}{x^2} \, dx\\ &=2 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx-5 \int \left (\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )-\frac {2 \exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2}\right ) \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx-\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+\int \left (4 \exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )+\frac {(5-2 e) \exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2}-\frac {5 \exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x}+\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) x\right ) \, dx-\int \left (-\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2}+\frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x}\right ) \, dx\\ &=2 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx+4 \int \exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \, dx-5 \int \exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \, dx-5 \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x} \, dx-5 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx+10 \int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-5 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+(5-2 e) \int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx-\int \frac {\exp \left (-15-\frac {5 e^{-1+x}}{x}-3 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right )}{x^2} \, dx+\int \exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) x \, dx+\int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x^2} \, dx-\int \frac {\exp \left (-14-\frac {5 e^{-1+x}}{x}-4 x+\frac {e^x \left (e^{-1+x}+3 x+x^2\right )}{x}+\frac {\left (5-e^x\right ) \log \left (x^2\right )}{x}\right ) \log \left (x^2\right )}{x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 51, normalized size = 1.55 \begin {gather*} e^{-14-\frac {5 e^{-1+x}}{x}+\frac {e^{-1+2 x}}{x}-5 x+e^x (3+x)} \left (x^2\right )^{\frac {5-e^x}{x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-5*E^(-1 + x) - 14*x - 5*x^2 + E^x*(E^(-1 + x) + 3*x + x^2) + (5 - E^x)*Log[x^2])/x)*(10 + E^(-
1 + x)*(5 - 5*x) - 5*x^2 + E^x*(-2 + 4*x^2 + x^3 + E^(-1 + x)*(-1 + 2*x)) + (-5 + E^x*(1 - x))*Log[x^2]))/x^2,
x]

[Out]

E^(-14 - (5*E^(-1 + x))/x + E^(-1 + 2*x)/x - 5*x + E^x*(3 + x))*(x^2)^((5 - E^x)/x)

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fricas [B]  time = 1.07, size = 60, normalized size = 1.82 \begin {gather*} e^{\left (-\frac {{\left ({\left (5 \, x^{2} + 14 \, x\right )} e - {\left ({\left (x^{2} + 3 \, x\right )} e - 5\right )} e^{x} - {\left (5 \, e - e^{\left (x + 1\right )}\right )} \log \left (x^{2}\right ) - e^{\left (2 \, x\right )}\right )} e^{\left (-1\right )}}{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x+1)*exp(x)-5)*log(x^2)+((2*x-1)*exp(x-1)+x^3+4*x^2-2)*exp(x)+(-5*x+5)*exp(x-1)-5*x^2+10)*exp(((
5-exp(x))*log(x^2)+(exp(x-1)+x^2+3*x)*exp(x)-5*exp(x-1)-5*x^2-14*x)/x)/x^2,x, algorithm="fricas")

[Out]

e^(-((5*x^2 + 14*x)*e - ((x^2 + 3*x)*e - 5)*e^x - (5*e - e^(x + 1))*log(x^2) - e^(2*x))*e^(-1)/x)

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giac [B]  time = 1.04, size = 53, normalized size = 1.61 \begin {gather*} e^{\left (x e^{x} - 5 \, x - \frac {e^{x} \log \left (x^{2}\right )}{x} + \frac {e^{\left (2 \, x - 1\right )}}{x} - \frac {5 \, e^{\left (x - 1\right )}}{x} + \frac {5 \, \log \left (x^{2}\right )}{x} + 3 \, e^{x} - 14\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x+1)*exp(x)-5)*log(x^2)+((2*x-1)*exp(x-1)+x^3+4*x^2-2)*exp(x)+(-5*x+5)*exp(x-1)-5*x^2+10)*exp(((
5-exp(x))*log(x^2)+(exp(x-1)+x^2+3*x)*exp(x)-5*exp(x-1)-5*x^2-14*x)/x)/x^2,x, algorithm="giac")

[Out]

e^(x*e^x - 5*x - e^x*log(x^2)/x + e^(2*x - 1)/x - 5*e^(x - 1)/x + 5*log(x^2)/x + 3*e^x - 14)

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maple [C]  time = 0.76, size = 156, normalized size = 4.73

method	result	size
risch	\({\mathrm e}^{-\frac {-i {\mathrm e}^{x} \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i {\mathrm e}^{x} \pi \mathrm {csgn}\left (i x^{2}\right )^{2} \mathrm {csgn}\left (i x \right )-i {\mathrm e}^{x} \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}+5 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}-10 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+5 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \,{\mathrm e}^{x} x^{2}+4 \,{\mathrm e}^{x} \ln \relax (x )-2 \,{\mathrm e}^{2 x -1}-6 \,{\mathrm e}^{x} x +10 x^{2}-20 \ln \relax (x )+10 \,{\mathrm e}^{x -1}+28 x}{2 x}}\)	\(156\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((1-x)*exp(x)-5)*ln(x^2)+((2*x-1)*exp(x-1)+x^3+4*x^2-2)*exp(x)+(-5*x+5)*exp(x-1)-5*x^2+10)*exp(((5-exp(x)
)*ln(x^2)+(exp(x-1)+x^2+3*x)*exp(x)-5*exp(x-1)-5*x^2-14*x)/x)/x^2,x,method=_RETURNVERBOSE)

[Out]

exp(-1/2*(-I*exp(x)*Pi*csgn(I*x^2)^3+2*I*exp(x)*Pi*csgn(I*x^2)^2*csgn(I*x)-I*exp(x)*Pi*csgn(I*x^2)*csgn(I*x)^2
+5*I*Pi*csgn(I*x^2)^3-10*I*Pi*csgn(I*x^2)^2*csgn(I*x)+5*I*Pi*csgn(I*x^2)*csgn(I*x)^2-2*exp(x)*x^2+4*exp(x)*ln(
x)-2*exp(2*x-1)-6*exp(x)*x+10*x^2-20*ln(x)+10*exp(x-1)+28*x)/x)

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maxima [A]  time = 0.77, size = 49, normalized size = 1.48 \begin {gather*} e^{\left (x e^{x} - 5 \, x - \frac {2 \, e^{x} \log \relax (x)}{x} + \frac {e^{\left (2 \, x - 1\right )}}{x} - \frac {5 \, e^{\left (x - 1\right )}}{x} + \frac {10 \, \log \relax (x)}{x} + 3 \, e^{x} - 14\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x+1)*exp(x)-5)*log(x^2)+((2*x-1)*exp(x-1)+x^3+4*x^2-2)*exp(x)+(-5*x+5)*exp(x-1)-5*x^2+10)*exp(((
5-exp(x))*log(x^2)+(exp(x-1)+x^2+3*x)*exp(x)-5*exp(x-1)-5*x^2-14*x)/x)/x^2,x, algorithm="maxima")

[Out]

e^(x*e^x - 5*x - 2*e^x*log(x)/x + e^(2*x - 1)/x - 5*e^(x - 1)/x + 10*log(x)/x + 3*e^x - 14)

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mupad [B]  time = 3.76, size = 50, normalized size = 1.52 \begin {gather*} {\mathrm {e}}^{x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-5\,x}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-1}}{x}}\,{\mathrm {e}}^{-14}\,{\mathrm {e}}^{3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-\frac {5\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^x}{x}}\,{\left (\frac {1}{x^2}\right )}^{\frac {{\mathrm {e}}^x-5}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(14*x + 5*exp(x - 1) - exp(x)*(3*x + exp(x - 1) + x^2) + 5*x^2 + log(x^2)*(exp(x) - 5))/x)*(log(x^2
)*(exp(x)*(x - 1) + 5) - exp(x)*(exp(x - 1)*(2*x - 1) + 4*x^2 + x^3 - 2) + exp(x - 1)*(5*x - 5) + 5*x^2 - 10))
/x^2,x)

[Out]

exp(x*exp(x))*exp(-5*x)*exp((exp(2*x)*exp(-1))/x)*exp(-14)*exp(3*exp(x))*exp(-(5*exp(-1)*exp(x))/x)*(1/x^2)^((
exp(x) - 5)/x)

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sympy [B]  time = 0.90, size = 46, normalized size = 1.39 \begin {gather*} e^{\frac {- 5 x^{2} - 14 x + \left (5 - e^{x}\right ) \log {\left (x^{2} \right )} + \left (x^{2} + 3 x + \frac {e^{x}}{e}\right ) e^{x} - \frac {5 e^{x}}{e}}{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-x+1)*exp(x)-5)*ln(x**2)+((2*x-1)*exp(x-1)+x**3+4*x**2-2)*exp(x)+(-5*x+5)*exp(x-1)-5*x**2+10)*exp
(((5-exp(x))*ln(x**2)+(exp(x-1)+x**2+3*x)*exp(x)-5*exp(x-1)-5*x**2-14*x)/x)/x**2,x)

[Out]

exp((-5*x**2 - 14*x + (5 - exp(x))*log(x**2) + (x**2 + 3*x + exp(-1)*exp(x))*exp(x) - 5*exp(-1)*exp(x))/x)

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