3.43.98 \(\int e^{1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4} (50+30 x-30 x^2+4 x^3) \, dx\)

Optimal. Leaf size=17 \[ e^{-24+e^{(5+(5-x) x)^2}} \]

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Rubi [F]  time = 1.04, 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 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) \left (50+30 x-30 x^2+4 x^3\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(1 + E^(25 + 50*x + 15*x^2 - 10*x^3 + x^4) + 50*x + 15*x^2 - 10*x^3 + x^4)*(50 + 30*x - 30*x^2 + 4*x^3),
x]

[Out]

50*Defer[Int][E^(1 + E^(25 + 50*x + 15*x^2 - 10*x^3 + x^4) + 50*x + 15*x^2 - 10*x^3 + x^4), x] + 30*Defer[Int]
[E^(1 + E^(25 + 50*x + 15*x^2 - 10*x^3 + x^4) + 50*x + 15*x^2 - 10*x^3 + x^4)*x, x] - 30*Defer[Int][E^(1 + E^(
25 + 50*x + 15*x^2 - 10*x^3 + x^4) + 50*x + 15*x^2 - 10*x^3 + x^4)*x^2, x] + 4*Defer[Int][E^(1 + E^(25 + 50*x
+ 15*x^2 - 10*x^3 + x^4) + 50*x + 15*x^2 - 10*x^3 + x^4)*x^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (50 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right )+30 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x-30 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^2+4 \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^3\right ) \, dx\\ &=4 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^3 \, dx+30 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x \, dx-30 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) x^2 \, dx+50 \int \exp \left (1+e^{25+50 x+15 x^2-10 x^3+x^4}+50 x+15 x^2-10 x^3+x^4\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.71, size = 16, normalized size = 0.94 \begin {gather*} e^{-24+e^{\left (-5-5 x+x^2\right )^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(1 + E^(25 + 50*x + 15*x^2 - 10*x^3 + x^4) + 50*x + 15*x^2 - 10*x^3 + x^4)*(50 + 30*x - 30*x^2 + 4
*x^3),x]

[Out]

E^(-24 + E^(-5 - 5*x + x^2)^2)

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fricas [A]  time = 0.60, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + 25\right )} - 24\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3-30*x^2+30*x+50)*exp(x^4-10*x^3+15*x^2+50*x+25)*exp(exp(x^4-10*x^3+15*x^2+50*x+25)-24),x, algo
rithm="fricas")

[Out]

e^(e^(x^4 - 10*x^3 + 15*x^2 + 50*x + 25) - 24)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 2 \, {\left (2 \, x^{3} - 15 \, x^{2} + 15 \, x + 25\right )} e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + 25\right )} + 1\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3-30*x^2+30*x+50)*exp(x^4-10*x^3+15*x^2+50*x+25)*exp(exp(x^4-10*x^3+15*x^2+50*x+25)-24),x, algo
rithm="giac")

[Out]

integrate(2*(2*x^3 - 15*x^2 + 15*x + 25)*e^(x^4 - 10*x^3 + 15*x^2 + 50*x + e^(x^4 - 10*x^3 + 15*x^2 + 50*x + 2
5) + 1), x)

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maple [A]  time = 0.06, size = 15, normalized size = 0.88

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{\left (x^{2}-5 x -5\right )^{2}}-24}\)	\(15\)
derivativedivides	\({\mathrm e}^{{\mathrm e}^{x^{4}-10 x^{3}+15 x^{2}+50 x +25}-24}\)	\(23\)
norman	\({\mathrm e}^{{\mathrm e}^{x^{4}-10 x^{3}+15 x^{2}+50 x +25}-24}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^3-30*x^2+30*x+50)*exp(x^4-10*x^3+15*x^2+50*x+25)*exp(exp(x^4-10*x^3+15*x^2+50*x+25)-24),x,method=_RET
URNVERBOSE)

[Out]

exp(exp((x^2-5*x-5)^2)-24)

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maxima [A]  time = 0.85, size = 22, normalized size = 1.29 \begin {gather*} e^{\left (e^{\left (x^{4} - 10 \, x^{3} + 15 \, x^{2} + 50 \, x + 25\right )} - 24\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3-30*x^2+30*x+50)*exp(x^4-10*x^3+15*x^2+50*x+25)*exp(exp(x^4-10*x^3+15*x^2+50*x+25)-24),x, algo
rithm="maxima")

[Out]

e^(e^(x^4 - 10*x^3 + 15*x^2 + 50*x + 25) - 24)

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mupad [B]  time = 3.14, size = 27, normalized size = 1.59 \begin {gather*} {\mathrm {e}}^{-24}\,{\mathrm {e}}^{{\mathrm {e}}^{50\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{25}\,{\mathrm {e}}^{-10\,x^3}\,{\mathrm {e}}^{15\,x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(exp(50*x + 15*x^2 - 10*x^3 + x^4 + 25) - 24)*exp(50*x + 15*x^2 - 10*x^3 + x^4 + 25)*(30*x - 30*x^2 + 4
*x^3 + 50),x)

[Out]

exp(-24)*exp(exp(50*x)*exp(x^4)*exp(25)*exp(-10*x^3)*exp(15*x^2))

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sympy [A]  time = 0.33, size = 22, normalized size = 1.29 \begin {gather*} e^{e^{x^{4} - 10 x^{3} + 15 x^{2} + 50 x + 25} - 24} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**3-30*x**2+30*x+50)*exp(x**4-10*x**3+15*x**2+50*x+25)*exp(exp(x**4-10*x**3+15*x**2+50*x+25)-24)
,x)

[Out]

exp(exp(x**4 - 10*x**3 + 15*x**2 + 50*x + 25) - 24)

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