3.91.68 \(\int \frac {-e^{\frac {1+e^{21}+2 x}{x}} x+e^{\frac {1+e^{21}+2 x}{x}} (-1-e^{21}-x) \log (x)}{x^3 \log ^2(x)} \, dx\)

Optimal. Leaf size=22 \[ \frac {e^{\frac {1+e^{21}+2 x}{x}}}{x \log (x)} \]

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Rubi [F]  time = 1.15, 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 {1+e^{21}+2 x}{x}} x+e^{\frac {1+e^{21}+2 x}{x}} \left (-1-e^{21}-x\right ) \log (x)}{x^3 \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-(E^((1 + E^21 + 2*x)/x)*x) + E^((1 + E^21 + 2*x)/x)*(-1 - E^21 - x)*Log[x])/(x^3*Log[x]^2),x]

[Out]

-Defer[Int][E^(2 + (1 + E^21)/x)/(x^2*Log[x]^2), x] - (1 + E^21)*Defer[Int][E^(2 + (1 + E^21)/x)/(x^3*Log[x]),
x] - Defer[Int][E^(2 + (1 + E^21)/x)/(x^2*Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2+\frac {1+e^{21}}{x}} \left (-x-\left (1+e^{21}+x\right ) \log (x)\right )}{x^3 \log ^2(x)} \, dx\\ &=\int \left (-\frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)}+\frac {e^{2+\frac {1+e^{21}}{x}} \left (-1-e^{21}-x\right )}{x^3 \log (x)}\right ) \, dx\\ &=-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)} \, dx+\int \frac {e^{2+\frac {1+e^{21}}{x}} \left (-1-e^{21}-x\right )}{x^3 \log (x)} \, dx\\ &=\int \left (\frac {e^{2+\frac {1+e^{21}}{x}} \left (-1-e^{21}\right )}{x^3 \log (x)}-\frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log (x)}\right ) \, dx-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)} \, dx\\ &=\left (-1-e^{21}\right ) \int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^3 \log (x)} \, dx-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log ^2(x)} \, dx-\int \frac {e^{2+\frac {1+e^{21}}{x}}}{x^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 21, normalized size = 0.95 \begin {gather*} \frac {e^{2+\frac {1+e^{21}}{x}}}{x \log (x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-(E^((1 + E^21 + 2*x)/x)*x) + E^((1 + E^21 + 2*x)/x)*(-1 - E^21 - x)*Log[x])/(x^3*Log[x]^2),x]

[Out]

E^(2 + (1 + E^21)/x)/(x*Log[x])

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fricas [A]  time = 0.57, size = 20, normalized size = 0.91 \begin {gather*} \frac {e^{\left (\frac {2 \, x + e^{21} + 1}{x}\right )}}{x \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(21)-x-1)*exp((exp(21)+2*x+1)/x)*log(x)-x*exp((exp(21)+2*x+1)/x))/x^3/log(x)^2,x, algorithm="f
ricas")

[Out]

e^((2*x + e^21 + 1)/x)/(x*log(x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left (x + e^{21} + 1\right )} e^{\left (\frac {2 \, x + e^{21} + 1}{x}\right )} \log \relax (x) + x e^{\left (\frac {2 \, x + e^{21} + 1}{x}\right )}}{x^{3} \log \relax (x)^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(21)-x-1)*exp((exp(21)+2*x+1)/x)*log(x)-x*exp((exp(21)+2*x+1)/x))/x^3/log(x)^2,x, algorithm="g
iac")

[Out]

integrate(-((x + e^21 + 1)*e^((2*x + e^21 + 1)/x)*log(x) + x*e^((2*x + e^21 + 1)/x))/(x^3*log(x)^2), x)

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maple [A]  time = 0.03, size = 21, normalized size = 0.95

method	result	size
risch	\(\frac {{\mathrm e}^{\frac {{\mathrm e}^{21}+2 x +1}{x}}}{x \ln \relax (x )}\)	\(21\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-exp(21)-x-1)*exp((exp(21)+2*x+1)/x)*ln(x)-x*exp((exp(21)+2*x+1)/x))/x^3/ln(x)^2,x,method=_RETURNVERBOSE
)

[Out]

exp((exp(21)+2*x+1)/x)/x/ln(x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\int \frac {{\left (x + e^{21} + 1\right )} e^{\left (\frac {2 \, x + e^{21} + 1}{x}\right )} \log \relax (x) + x e^{\left (\frac {2 \, x + e^{21} + 1}{x}\right )}}{x^{3} \log \relax (x)^{2}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(21)-x-1)*exp((exp(21)+2*x+1)/x)*log(x)-x*exp((exp(21)+2*x+1)/x))/x^3/log(x)^2,x, algorithm="m
axima")

[Out]

-integrate(((x + e^21 + 1)*e^((2*x + e^21 + 1)/x)*log(x) + x*e^((2*x + e^21 + 1)/x))/(x^3*log(x)^2), x)

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mupad [B]  time = 7.52, size = 21, normalized size = 0.95 \begin {gather*} \frac {{\mathrm {e}}^{\frac {{\mathrm {e}}^{21}}{x}}\,{\mathrm {e}}^{1/x}\,{\mathrm {e}}^2}{x\,\ln \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x*exp((2*x + exp(21) + 1)/x) + exp((2*x + exp(21) + 1)/x)*log(x)*(x + exp(21) + 1))/(x^3*log(x)^2),x)

[Out]

(exp(exp(21)/x)*exp(1/x)*exp(2))/(x*log(x))

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sympy [A]  time = 0.29, size = 15, normalized size = 0.68 \begin {gather*} \frac {e^{\frac {2 x + 1 + e^{21}}{x}}}{x \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-exp(21)-x-1)*exp((exp(21)+2*x+1)/x)*ln(x)-x*exp((exp(21)+2*x+1)/x))/x**3/ln(x)**2,x)

[Out]

exp((2*x + 1 + exp(21))/x)/(x*log(x))

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