3.91.26 \(\int \frac {1+4 e^x+e^{225-90 e^x+9 e^{2 x}} (2 e^x-90 e^{2 x}+18 e^{3 x})+x}{2 e^x+e^{225-90 e^x+9 e^{2 x}+x}+x} \, dx\)

Optimal. Leaf size=26 \[ 2+e^2+x+\log \left (e^x \left (2+e^{9 \left (-5+e^x\right )^2}\right )+x\right ) \]

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Rubi [F]  time = 180.00, 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*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1 + 4*E^x + E^(225 - 90*E^x + 9*E^(2*x))*(2*E^x - 90*E^(2*x) + 18*E^(3*x)) + x)/(2*E^x + E^(225 - 90*E^x
+ 9*E^(2*x) + x) + x),x]

[Out]

$Aborted

Rubi steps

Aborted

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Mathematica [A]  time = 0.13, size = 27, normalized size = 1.04 \begin {gather*} x+\log \left (2 e^x+e^{225-90 e^x+9 e^{2 x}+x}+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1 + 4*E^x + E^(225 - 90*E^x + 9*E^(2*x))*(2*E^x - 90*E^(2*x) + 18*E^(3*x)) + x)/(2*E^x + E^(225 - 9
0*E^x + 9*E^(2*x) + x) + x),x]

[Out]

x + Log[2*E^x + E^(225 - 90*E^x + 9*E^(2*x) + x) + x]

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fricas [A]  time = 0.49, size = 23, normalized size = 0.88 \begin {gather*} x + \log \left (x + e^{\left (x + 9 \, e^{\left (2 \, x\right )} - 90 \, e^{x} + 225\right )} + 2 \, e^{x}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*exp(x)^3-90*exp(x)^2+2*exp(x))*exp(9*exp(x)^2-90*exp(x)+225)+4*exp(x)+x+1)/(exp(x)*exp(9*exp(x)
^2-90*exp(x)+225)+2*exp(x)+x),x, algorithm="fricas")

[Out]

x + log(x + e^(x + 9*e^(2*x) - 90*e^x + 225) + 2*e^x)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2 \, {\left (9 \, e^{\left (3 \, x\right )} - 45 \, e^{\left (2 \, x\right )} + e^{x}\right )} e^{\left (9 \, e^{\left (2 \, x\right )} - 90 \, e^{x} + 225\right )} + x + 4 \, e^{x} + 1}{x + e^{\left (x + 9 \, e^{\left (2 \, x\right )} - 90 \, e^{x} + 225\right )} + 2 \, e^{x}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*exp(x)^3-90*exp(x)^2+2*exp(x))*exp(9*exp(x)^2-90*exp(x)+225)+4*exp(x)+x+1)/(exp(x)*exp(9*exp(x)
^2-90*exp(x)+225)+2*exp(x)+x),x, algorithm="giac")

[Out]

integrate((2*(9*e^(3*x) - 45*e^(2*x) + e^x)*e^(9*e^(2*x) - 90*e^x + 225) + x + 4*e^x + 1)/(x + e^(x + 9*e^(2*x
) - 90*e^x + 225) + 2*e^x), x)

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maple [A]  time = 0.07, size = 26, normalized size = 1.00

method	result	size
norman	\(x +\ln \left ({\mathrm e}^{x} {\mathrm e}^{9 \,{\mathrm e}^{2 x}-90 \,{\mathrm e}^{x}+225}+2 \,{\mathrm e}^{x}+x \right )\)	\(26\)
risch	\(2 x -225+\ln \left ({\mathrm e}^{9 \,{\mathrm e}^{2 x}-90 \,{\mathrm e}^{x}+225}+\left (2 \,{\mathrm e}^{x}+x \right ) {\mathrm e}^{-x}\right )\)	\(32\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((18*exp(x)^3-90*exp(x)^2+2*exp(x))*exp(9*exp(x)^2-90*exp(x)+225)+4*exp(x)+x+1)/(exp(x)*exp(9*exp(x)^2-90*
exp(x)+225)+2*exp(x)+x),x,method=_RETURNVERBOSE)

[Out]

x+ln(exp(x)*exp(9*exp(x)^2-90*exp(x)+225)+2*exp(x)+x)

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maxima [A]  time = 0.40, size = 39, normalized size = 1.50 \begin {gather*} 2 \, x - 90 \, e^{x} + \log \left ({\left ({\left (x + 2 \, e^{x}\right )} e^{\left (90 \, e^{x}\right )} + e^{\left (x + 9 \, e^{\left (2 \, x\right )} + 225\right )}\right )} e^{\left (-x - 225\right )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*exp(x)^3-90*exp(x)^2+2*exp(x))*exp(9*exp(x)^2-90*exp(x)+225)+4*exp(x)+x+1)/(exp(x)*exp(9*exp(x)
^2-90*exp(x)+225)+2*exp(x)+x),x, algorithm="maxima")

[Out]

2*x - 90*e^x + log(((x + 2*e^x)*e^(90*e^x) + e^(x + 9*e^(2*x) + 225))*e^(-x - 225))

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mupad [B]  time = 7.00, size = 26, normalized size = 1.00 \begin {gather*} x+\ln \left (x+2\,{\mathrm {e}}^x+{\mathrm {e}}^{9\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{225}\,{\mathrm {e}}^{-90\,{\mathrm {e}}^x}\,{\mathrm {e}}^x\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + 4*exp(x) + exp(9*exp(2*x) - 90*exp(x) + 225)*(18*exp(3*x) - 90*exp(2*x) + 2*exp(x)) + 1)/(x + 2*exp(x
) + exp(9*exp(2*x) - 90*exp(x) + 225)*exp(x)),x)

[Out]

x + log(x + 2*exp(x) + exp(9*exp(2*x))*exp(225)*exp(-90*exp(x))*exp(x))

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sympy [A]  time = 0.28, size = 29, normalized size = 1.12 \begin {gather*} 2 x + \log {\left (\left (x + 2 e^{x}\right ) e^{- x} + e^{9 e^{2 x} - 90 e^{x} + 225} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((18*exp(x)**3-90*exp(x)**2+2*exp(x))*exp(9*exp(x)**2-90*exp(x)+225)+4*exp(x)+x+1)/(exp(x)*exp(9*exp
(x)**2-90*exp(x)+225)+2*exp(x)+x),x)

[Out]

2*x + log((x + 2*exp(x))*exp(-x) + exp(9*exp(2*x) - 90*exp(x) + 225))

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