3.36.74 \(\int \frac {e^{1+x+x^4} (-144+16 x+16 x^2+192 x^4+64 x^5)}{x^4} \, dx\)

Optimal. Leaf size=20 \[ \frac {16 e^{1+x+x^4} \left (1+\frac {3}{x}\right )}{x^2} \]

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Rubi [F]  time = 0.42, 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^{1+x+x^4} \left (-144+16 x+16 x^2+192 x^4+64 x^5\right )}{x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(1 + x + x^4)*(-144 + 16*x + 16*x^2 + 192*x^4 + 64*x^5))/x^4,x]

[Out]

192*Defer[Int][E^(1 + x + x^4), x] - 144*Defer[Int][E^(1 + x + x^4)/x^4, x] + 16*Defer[Int][E^(1 + x + x^4)/x^
3, x] + 16*Defer[Int][E^(1 + x + x^4)/x^2, x] + 64*Defer[Int][E^(1 + x + x^4)*x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {16 e^{1+x+x^4} \left (-9+x+x^2+12 x^4+4 x^5\right )}{x^4} \, dx\\ &=16 \int \frac {e^{1+x+x^4} \left (-9+x+x^2+12 x^4+4 x^5\right )}{x^4} \, dx\\ &=16 \int \left (12 e^{1+x+x^4}-\frac {9 e^{1+x+x^4}}{x^4}+\frac {e^{1+x+x^4}}{x^3}+\frac {e^{1+x+x^4}}{x^2}+4 e^{1+x+x^4} x\right ) \, dx\\ &=16 \int \frac {e^{1+x+x^4}}{x^3} \, dx+16 \int \frac {e^{1+x+x^4}}{x^2} \, dx+64 \int e^{1+x+x^4} x \, dx-144 \int \frac {e^{1+x+x^4}}{x^4} \, dx+192 \int e^{1+x+x^4} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 16, normalized size = 0.80 \begin {gather*} \frac {16 e^{1+x+x^4} (3+x)}{x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(1 + x + x^4)*(-144 + 16*x + 16*x^2 + 192*x^4 + 64*x^5))/x^4,x]

[Out]

(16*E^(1 + x + x^4)*(3 + x))/x^3

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fricas [A]  time = 0.64, size = 15, normalized size = 0.75 \begin {gather*} \frac {16 \, {\left (x + 3\right )} e^{\left (x^{4} + x + 1\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*x^5+192*x^4+16*x^2+16*x-144)*exp(1)*exp(x^4+x)/x^4,x, algorithm="fricas")

[Out]

16*(x + 3)*e^(x^4 + x + 1)/x^3

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giac [A]  time = 0.15, size = 24, normalized size = 1.20 \begin {gather*} \frac {16 \, {\left (x e^{\left (x^{4} + x + 1\right )} + 3 \, e^{\left (x^{4} + x + 1\right )}\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*x^5+192*x^4+16*x^2+16*x-144)*exp(1)*exp(x^4+x)/x^4,x, algorithm="giac")

[Out]

16*(x*e^(x^4 + x + 1) + 3*e^(x^4 + x + 1))/x^3

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maple [A]  time = 0.05, size = 16, normalized size = 0.80

method	result	size
gosper	\(\frac {16 \,{\mathrm e}^{x^{4}+x +1} \left (3+x \right )}{x^{3}}\)	\(16\)
risch	\(\frac {16 \,{\mathrm e}^{x^{4}+x +1} \left (3+x \right )}{x^{3}}\)	\(16\)
norman	\(\frac {48 \,{\mathrm e} \,{\mathrm e}^{x^{4}+x}+16 x \,{\mathrm e} \,{\mathrm e}^{x^{4}+x}}{x^{3}}\)	\(27\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((64*x^5+192*x^4+16*x^2+16*x-144)*exp(1)*exp(x^4+x)/x^4,x,method=_RETURNVERBOSE)

[Out]

16*exp(x^4+x+1)*(3+x)/x^3

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maxima [A]  time = 0.47, size = 20, normalized size = 1.00 \begin {gather*} \frac {16 \, {\left (x e + 3 \, e\right )} e^{\left (x^{4} + x\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*x^5+192*x^4+16*x^2+16*x-144)*exp(1)*exp(x^4+x)/x^4,x, algorithm="maxima")

[Out]

16*(x*e + 3*e)*e^(x^4 + x)/x^3

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mupad [B]  time = 0.08, size = 15, normalized size = 0.75 \begin {gather*} \frac {16\,{\mathrm {e}}^{x^4+x+1}\,\left (x+3\right )}{x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x + x^4)*exp(1)*(16*x + 16*x^2 + 192*x^4 + 64*x^5 - 144))/x^4,x)

[Out]

(16*exp(x + x^4 + 1)*(x + 3))/x^3

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sympy [A]  time = 0.14, size = 20, normalized size = 1.00 \begin {gather*} \frac {\left (16 e x + 48 e\right ) e^{x^{4} + x}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((64*x**5+192*x**4+16*x**2+16*x-144)*exp(1)*exp(x**4+x)/x**4,x)

[Out]

(16*E*x + 48*E)*exp(x**4 + x)/x**3

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