3.24.79 \(\int \frac {e^{\frac {1-110 x-17 x^2+x^3}{-22+x}} (2419+748 x-83 x^2+2 x^3)}{484-44 x+x^2} \, dx\)

Optimal. Leaf size=19 \[ e^{x \left (5-\frac {1}{(22-x) x}+x\right )} \]

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Rubi [F]  time = 0.44, 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 {1-110 x-17 x^2+x^3}{-22+x}} \left (2419+748 x-83 x^2+2 x^3\right )}{484-44 x+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((1 - 110*x - 17*x^2 + x^3)/(-22 + x))*(2419 + 748*x - 83*x^2 + 2*x^3))/(484 - 44*x + x^2),x]

[Out]

5*Defer[Int][E^((1 - 110*x - 17*x^2 + x^3)/(-22 + x)), x] - Defer[Int][E^((1 - 110*x - 17*x^2 + x^3)/(-22 + x)
)/(-22 + x)^2, x] + 2*Defer[Int][E^((1 - 110*x - 17*x^2 + x^3)/(-22 + x))*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {1-110 x-17 x^2+x^3}{-22+x}} \left (2419+748 x-83 x^2+2 x^3\right )}{(-22+x)^2} \, dx\\ &=\int \left (5 e^{\frac {1-110 x-17 x^2+x^3}{-22+x}}-\frac {e^{\frac {1-110 x-17 x^2+x^3}{-22+x}}}{(-22+x)^2}+2 e^{\frac {1-110 x-17 x^2+x^3}{-22+x}} x\right ) \, dx\\ &=2 \int e^{\frac {1-110 x-17 x^2+x^3}{-22+x}} x \, dx+5 \int e^{\frac {1-110 x-17 x^2+x^3}{-22+x}} \, dx-\int \frac {e^{\frac {1-110 x-17 x^2+x^3}{-22+x}}}{(-22+x)^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.16, size = 14, normalized size = 0.74 \begin {gather*} e^{\frac {1}{-22+x}+5 x+x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((1 - 110*x - 17*x^2 + x^3)/(-22 + x))*(2419 + 748*x - 83*x^2 + 2*x^3))/(484 - 44*x + x^2),x]

[Out]

E^((-22 + x)^(-1) + 5*x + x^2)

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fricas [A]  time = 0.46, size = 20, normalized size = 1.05 \begin {gather*} e^{\left (\frac {x^{3} - 17 \, x^{2} - 110 \, x + 1}{x - 22}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^3-83*x^2+748*x+2419)*exp((x^3-17*x^2-110*x+1)/(x-22))/(x^2-44*x+484),x, algorithm="fricas")

[Out]

e^((x^3 - 17*x^2 - 110*x + 1)/(x - 22))

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giac [B]  time = 0.19, size = 34, normalized size = 1.79 \begin {gather*} e^{\left (\frac {x^{3}}{x - 22} - \frac {17 \, x^{2}}{x - 22} - \frac {110 \, x}{x - 22} + \frac {1}{x - 22}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^3-83*x^2+748*x+2419)*exp((x^3-17*x^2-110*x+1)/(x-22))/(x^2-44*x+484),x, algorithm="giac")

[Out]

e^(x^3/(x - 22) - 17*x^2/(x - 22) - 110*x/(x - 22) + 1/(x - 22))

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maple [A]  time = 0.54, size = 21, normalized size = 1.11

method	result	size
gosper	\({\mathrm e}^{\frac {x^{3}-17 x^{2}-110 x +1}{x -22}}\)	\(21\)
risch	\({\mathrm e}^{\frac {x^{3}-17 x^{2}-110 x +1}{x -22}}\)	\(21\)
norman	\(\frac {x \,{\mathrm e}^{\frac {x^{3}-17 x^{2}-110 x +1}{x -22}}-22 \,{\mathrm e}^{\frac {x^{3}-17 x^{2}-110 x +1}{x -22}}}{x -22}\)	\(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^3-83*x^2+748*x+2419)*exp((x^3-17*x^2-110*x+1)/(x-22))/(x^2-44*x+484),x,method=_RETURNVERBOSE)

[Out]

exp((x^3-17*x^2-110*x+1)/(x-22))

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maxima [A]  time = 0.69, size = 13, normalized size = 0.68 \begin {gather*} e^{\left (x^{2} + 5 \, x + \frac {1}{x - 22}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^3-83*x^2+748*x+2419)*exp((x^3-17*x^2-110*x+1)/(x-22))/(x^2-44*x+484),x, algorithm="maxima")

[Out]

e^(x^2 + 5*x + 1/(x - 22))

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mupad [B]  time = 0.13, size = 37, normalized size = 1.95 \begin {gather*} {\mathrm {e}}^{-\frac {110\,x}{x-22}}\,{\mathrm {e}}^{\frac {1}{x-22}}\,{\mathrm {e}}^{\frac {x^3}{x-22}}\,{\mathrm {e}}^{-\frac {17\,x^2}{x-22}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(110*x + 17*x^2 - x^3 - 1)/(x - 22))*(748*x - 83*x^2 + 2*x^3 + 2419))/(x^2 - 44*x + 484),x)

[Out]

exp(-(110*x)/(x - 22))*exp(1/(x - 22))*exp(x^3/(x - 22))*exp(-(17*x^2)/(x - 22))

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sympy [A]  time = 0.18, size = 17, normalized size = 0.89 \begin {gather*} e^{\frac {x^{3} - 17 x^{2} - 110 x + 1}{x - 22}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**3-83*x**2+748*x+2419)*exp((x**3-17*x**2-110*x+1)/(x-22))/(x**2-44*x+484),x)

[Out]

exp((x**3 - 17*x**2 - 110*x + 1)/(x - 22))

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