3.74.5 \(\int e^{-e^x} (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} (-4 x^3+10 x^4)) \, dx\)

Optimal. Leaf size=20 \[ x^4 \left (-1+2 x+e^{21-e^x} x\right ) \]

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Rubi [F]  time = 0.21, 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 e^{-e^x} \left (5 e^{21} x^4-e^{21+x} x^5+e^{e^x} \left (-4 x^3+10 x^4\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(5*E^21*x^4 - E^(21 + x)*x^5 + E^E^x*(-4*x^3 + 10*x^4))/E^E^x,x]

[Out]

-x^4 + 2*x^5 + 5*Defer[Int][E^(21 - E^x)*x^4, x] - Defer[Int][E^(21 - E^x + x)*x^5, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (5 e^{21-e^x} x^4-e^{21-e^x+x} x^5+2 x^3 (-2+5 x)\right ) \, dx\\ &=2 \int x^3 (-2+5 x) \, dx+5 \int e^{21-e^x} x^4 \, dx-\int e^{21-e^x+x} x^5 \, dx\\ &=2 \int \left (-2 x^3+5 x^4\right ) \, dx+5 \int e^{21-e^x} x^4 \, dx-\int e^{21-e^x+x} x^5 \, dx\\ &=-x^4+2 x^5+5 \int e^{21-e^x} x^4 \, dx-\int e^{21-e^x+x} x^5 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 19, normalized size = 0.95 \begin {gather*} x^4 \left (-1+\left (2+e^{21-e^x}\right ) x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(5*E^21*x^4 - E^(21 + x)*x^5 + E^E^x*(-4*x^3 + 10*x^4))/E^E^x,x]

[Out]

x^4*(-1 + (2 + E^(21 - E^x))*x)

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fricas [A]  time = 1.22, size = 28, normalized size = 1.40 \begin {gather*} {\left (x^{5} e^{21} + {\left (2 \, x^{5} - x^{4}\right )} e^{\left (e^{x}\right )}\right )} e^{\left (-e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x^4-4*x^3)*exp(exp(x))-x^5*exp(21)*exp(x)+5*x^4*exp(21))/exp(exp(x)),x, algorithm="fricas")

[Out]

(x^5*e^21 + (2*x^5 - x^4)*e^(e^x))*e^(-e^x)

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giac [A]  time = 0.12, size = 22, normalized size = 1.10 \begin {gather*} x^{5} e^{\left (-e^{x} + 21\right )} + 2 \, x^{5} - x^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x^4-4*x^3)*exp(exp(x))-x^5*exp(21)*exp(x)+5*x^4*exp(21))/exp(exp(x)),x, algorithm="giac")

[Out]

x^5*e^(-e^x + 21) + 2*x^5 - x^4

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maple [A]  time = 0.07, size = 23, normalized size = 1.15

method	result	size
risch	\(2 x^{5}-x^{4}+x^{5} {\mathrm e}^{21-{\mathrm e}^{x}}\)	\(23\)
norman	\(\left ({\mathrm e}^{21} x^{5}-x^{4} {\mathrm e}^{{\mathrm e}^{x}}+2 x^{5} {\mathrm e}^{{\mathrm e}^{x}}\right ) {\mathrm e}^{-{\mathrm e}^{x}}\)	\(30\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((10*x^4-4*x^3)*exp(exp(x))-x^5*exp(21)*exp(x)+5*x^4*exp(21))/exp(exp(x)),x,method=_RETURNVERBOSE)

[Out]

2*x^5-x^4+x^5*exp(21-exp(x))

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maxima [A]  time = 0.41, size = 22, normalized size = 1.10 \begin {gather*} x^{5} e^{\left (-e^{x} + 21\right )} + 2 \, x^{5} - x^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x^4-4*x^3)*exp(exp(x))-x^5*exp(21)*exp(x)+5*x^4*exp(21))/exp(exp(x)),x, algorithm="maxima")

[Out]

x^5*e^(-e^x + 21) + 2*x^5 - x^4

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mupad [B]  time = 4.43, size = 22, normalized size = 1.10 \begin {gather*} 2\,x^5-x^4+x^5\,{\mathrm {e}}^{21}\,{\mathrm {e}}^{-{\mathrm {e}}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-exp(x))*(exp(exp(x))*(4*x^3 - 10*x^4) - 5*x^4*exp(21) + x^5*exp(21)*exp(x)),x)

[Out]

2*x^5 - x^4 + x^5*exp(21)*exp(-exp(x))

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sympy [A]  time = 0.18, size = 19, normalized size = 0.95 \begin {gather*} 2 x^{5} + x^{5} e^{21} e^{- e^{x}} - x^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((10*x**4-4*x**3)*exp(exp(x))-x**5*exp(21)*exp(x)+5*x**4*exp(21))/exp(exp(x)),x)

[Out]

2*x**5 + x**5*exp(21)*exp(-exp(x)) - x**4

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