3.58.87 \(\int \frac {2 x+e^{26+e^{2 x}+x} (3-x-2 e^{2 x} x)}{x^4} \, dx\)

Optimal. Leaf size=19 \[ 10-\frac {e^{26+e^{2 x}+x}+x}{x^3} \]

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Rubi [F]  time = 0.33, 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 {2 x+e^{26+e^{2 x}+x} \left (3-x-2 e^{2 x} x\right )}{x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(2*x + E^(26 + E^(2*x) + x)*(3 - x - 2*E^(2*x)*x))/x^4,x]

[Out]

-x^(-2) + 3*Defer[Int][E^(26 + E^(2*x) + x)/x^4, x] - Defer[Int][E^(26 + E^(2*x) + x)/x^3, x] - 2*Defer[Int][E
^(26 + E^(2*x) + 3*x)/x^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {e^{26+e^{2 x}+x} (-3+x)}{x^4}+\frac {2}{x^3}-\frac {2 e^{26+e^{2 x}+3 x}}{x^3}\right ) \, dx\\ &=-\frac {1}{x^2}-2 \int \frac {e^{26+e^{2 x}+3 x}}{x^3} \, dx-\int \frac {e^{26+e^{2 x}+x} (-3+x)}{x^4} \, dx\\ &=-\frac {1}{x^2}-2 \int \frac {e^{26+e^{2 x}+3 x}}{x^3} \, dx-\int \left (-\frac {3 e^{26+e^{2 x}+x}}{x^4}+\frac {e^{26+e^{2 x}+x}}{x^3}\right ) \, dx\\ &=-\frac {1}{x^2}-2 \int \frac {e^{26+e^{2 x}+3 x}}{x^3} \, dx+3 \int \frac {e^{26+e^{2 x}+x}}{x^4} \, dx-\int \frac {e^{26+e^{2 x}+x}}{x^3} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 17, normalized size = 0.89 \begin {gather*} -\frac {e^{26+e^{2 x}+x}+x}{x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*x + E^(26 + E^(2*x) + x)*(3 - x - 2*E^(2*x)*x))/x^4,x]

[Out]

-((E^(26 + E^(2*x) + x) + x)/x^3)

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fricas [A]  time = 0.53, size = 15, normalized size = 0.79 \begin {gather*} -\frac {x + e^{\left (x + e^{\left (2 \, x\right )} + 26\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(x)^2+3-x)*exp(exp(x)^2+x+26)+2*x)/x^4,x, algorithm="fricas")

[Out]

-(x + e^(x + e^(2*x) + 26))/x^3

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giac [A]  time = 0.22, size = 15, normalized size = 0.79 \begin {gather*} -\frac {x + e^{\left (x + e^{\left (2 \, x\right )} + 26\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(x)^2+3-x)*exp(exp(x)^2+x+26)+2*x)/x^4,x, algorithm="giac")

[Out]

-(x + e^(x + e^(2*x) + 26))/x^3

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maple [A]  time = 0.07, size = 19, normalized size = 1.00

method	result	size
norman	\(\frac {-x -{\mathrm e}^{{\mathrm e}^{2 x}+x +26}}{x^{3}}\)	\(19\)
risch	\(-\frac {1}{x^{2}}-\frac {{\mathrm e}^{{\mathrm e}^{2 x}+x +26}}{x^{3}}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x*exp(x)^2+3-x)*exp(exp(x)^2+x+26)+2*x)/x^4,x,method=_RETURNVERBOSE)

[Out]

(-x-exp(exp(x)^2+x+26))/x^3

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maxima [A]  time = 0.43, size = 19, normalized size = 1.00 \begin {gather*} -\frac {1}{x^{2}} - \frac {e^{\left (x + e^{\left (2 \, x\right )} + 26\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(x)^2+3-x)*exp(exp(x)^2+x+26)+2*x)/x^4,x, algorithm="maxima")

[Out]

-1/x^2 - e^(x + e^(2*x) + 26)/x^3

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mupad [B]  time = 4.06, size = 17, normalized size = 0.89 \begin {gather*} -\frac {x+{\mathrm {e}}^{26}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^x}{x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x - exp(x + exp(2*x) + 26)*(x + 2*x*exp(2*x) - 3))/x^4,x)

[Out]

-(x + exp(26)*exp(exp(2*x))*exp(x))/x^3

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sympy [A]  time = 0.12, size = 19, normalized size = 1.00 \begin {gather*} - \frac {1}{x^{2}} - \frac {e^{x + e^{2 x} + 26}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x*exp(x)**2+3-x)*exp(exp(x)**2+x+26)+2*x)/x**4,x)

[Out]

-1/x**2 - exp(x + exp(2*x) + 26)/x**3

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