3.29.45 \(\int \frac {e^{\frac {-144+36 x+5 x^3}{-4+x}} (-240 x^2+40 x^3)}{16-8 x+x^2} \, dx\)

Optimal. Leaf size=28 \[ 4 e^{36+5 x^2 \left (x-\frac {(5-x) x}{4-x}\right )} \]

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Rubi [F]  time = 0.56, 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 {-144+36 x+5 x^3}{-4+x}} \left (-240 x^2+40 x^3\right )}{16-8 x+x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^((-144 + 36*x + 5*x^3)/(-4 + x))*(-240*x^2 + 40*x^3))/(16 - 8*x + x^2),x]

[Out]

80*Defer[Int][E^((-144 + 36*x + 5*x^3)/(-4 + x)), x] - 1280*Defer[Int][E^((-144 + 36*x + 5*x^3)/(-4 + x))/(-4
+ x)^2, x] + 40*Defer[Int][E^((-144 + 36*x + 5*x^3)/(-4 + x))*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{\frac {-144+36 x+5 x^3}{-4+x}} \left (-240 x^2+40 x^3\right )}{(-4+x)^2} \, dx\\ &=\int \frac {e^{\frac {-144+36 x+5 x^3}{-4+x}} x^2 (-240+40 x)}{(-4+x)^2} \, dx\\ &=\int \left (80 e^{\frac {-144+36 x+5 x^3}{-4+x}}-\frac {1280 e^{\frac {-144+36 x+5 x^3}{-4+x}}}{(-4+x)^2}+40 e^{\frac {-144+36 x+5 x^3}{-4+x}} x\right ) \, dx\\ &=40 \int e^{\frac {-144+36 x+5 x^3}{-4+x}} x \, dx+80 \int e^{\frac {-144+36 x+5 x^3}{-4+x}} \, dx-1280 \int \frac {e^{\frac {-144+36 x+5 x^3}{-4+x}}}{(-4+x)^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 20, normalized size = 0.71 \begin {gather*} 4 e^{\frac {-144+36 x+5 x^3}{-4+x}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((-144 + 36*x + 5*x^3)/(-4 + x))*(-240*x^2 + 40*x^3))/(16 - 8*x + x^2),x]

[Out]

4*E^((-144 + 36*x + 5*x^3)/(-4 + x))

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fricas [A]  time = 0.43, size = 19, normalized size = 0.68 \begin {gather*} 4 \, e^{\left (\frac {5 \, x^{3} + 36 \, x - 144}{x - 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x^3-240*x^2)*exp((5*x^3+36*x-144)/(x-4))/(x^2-8*x+16),x, algorithm="fricas")

[Out]

4*e^((5*x^3 + 36*x - 144)/(x - 4))

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giac [A]  time = 0.48, size = 29, normalized size = 1.04 \begin {gather*} 4 \, e^{\left (\frac {5 \, x^{3}}{x - 4} + \frac {36 \, x}{x - 4} - \frac {144}{x - 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x^3-240*x^2)*exp((5*x^3+36*x-144)/(x-4))/(x^2-8*x+16),x, algorithm="giac")

[Out]

4*e^(5*x^3/(x - 4) + 36*x/(x - 4) - 144/(x - 4))

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maple [A]  time = 0.53, size = 20, normalized size = 0.71

method	result	size
gosper	\(4 \,{\mathrm e}^{\frac {5 x^{3}+36 x -144}{x -4}}\)	\(20\)
risch	\(4 \,{\mathrm e}^{\frac {5 x^{3}+36 x -144}{x -4}}\)	\(20\)
norman	\(\frac {4 x \,{\mathrm e}^{\frac {5 x^{3}+36 x -144}{x -4}}-16 \,{\mathrm e}^{\frac {5 x^{3}+36 x -144}{x -4}}}{x -4}\)	\(47\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((40*x^3-240*x^2)*exp((5*x^3+36*x-144)/(x-4))/(x^2-8*x+16),x,method=_RETURNVERBOSE)

[Out]

4*exp((5*x^3+36*x-144)/(x-4))

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maxima [A]  time = 0.66, size = 20, normalized size = 0.71 \begin {gather*} 4 \, e^{\left (5 \, x^{2} + 20 \, x + \frac {320}{x - 4} + 116\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x^3-240*x^2)*exp((5*x^3+36*x-144)/(x-4))/(x^2-8*x+16),x, algorithm="maxima")

[Out]

4*e^(5*x^2 + 20*x + 320/(x - 4) + 116)

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mupad [B]  time = 1.73, size = 19, normalized size = 0.68 \begin {gather*} 4\,{\mathrm {e}}^{\frac {5\,x^3+36\,x-144}{x-4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((36*x + 5*x^3 - 144)/(x - 4))*(240*x^2 - 40*x^3))/(x^2 - 8*x + 16),x)

[Out]

4*exp((36*x + 5*x^3 - 144)/(x - 4))

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sympy [A]  time = 0.16, size = 15, normalized size = 0.54 \begin {gather*} 4 e^{\frac {5 x^{3} + 36 x - 144}{x - 4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((40*x**3-240*x**2)*exp((5*x**3+36*x-144)/(x-4))/(x**2-8*x+16),x)

[Out]

4*exp((5*x**3 + 36*x - 144)/(x - 4))

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