3.59.27 \(\int (5+4 x+e^8 (-28561-35152 x-26364 x^2-8112 x^3-5070 x^4-624 x^5-364 x^6-16 x^7-9 x^8)) \, dx\)

Optimal. Leaf size=23 \[ 1+x+(2+x) \left (2 x-e^8 \left (13+x^2\right )^4\right ) \]

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Rubi [B]  time = 0.02, antiderivative size = 79, normalized size of antiderivative = 3.43, number of steps used = 2, number of rules used = 0, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -e^8 x^9-2 e^8 x^8-52 e^8 x^7-104 e^8 x^6-1014 e^8 x^5-2028 e^8 x^4-8788 e^8 x^3-17576 e^8 x^2+2 x^2-28561 e^8 x+5 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[5 + 4*x + E^8*(-28561 - 35152*x - 26364*x^2 - 8112*x^3 - 5070*x^4 - 624*x^5 - 364*x^6 - 16*x^7 - 9*x^8),x]

[Out]

5*x - 28561*E^8*x + 2*x^2 - 17576*E^8*x^2 - 8788*E^8*x^3 - 2028*E^8*x^4 - 1014*E^8*x^5 - 104*E^8*x^6 - 52*E^8*
x^7 - 2*E^8*x^8 - E^8*x^9

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=5 x+2 x^2+e^8 \int \left (-28561-35152 x-26364 x^2-8112 x^3-5070 x^4-624 x^5-364 x^6-16 x^7-9 x^8\right ) \, dx\\ &=5 x-28561 e^8 x+2 x^2-17576 e^8 x^2-8788 e^8 x^3-2028 e^8 x^4-1014 e^8 x^5-104 e^8 x^6-52 e^8 x^7-2 e^8 x^8-e^8 x^9\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.00, size = 79, normalized size = 3.43 \begin {gather*} 5 x-28561 e^8 x+2 x^2-17576 e^8 x^2-8788 e^8 x^3-2028 e^8 x^4-1014 e^8 x^5-104 e^8 x^6-52 e^8 x^7-2 e^8 x^8-e^8 x^9 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[5 + 4*x + E^8*(-28561 - 35152*x - 26364*x^2 - 8112*x^3 - 5070*x^4 - 624*x^5 - 364*x^6 - 16*x^7 - 9*x
^8),x]

[Out]

5*x - 28561*E^8*x + 2*x^2 - 17576*E^8*x^2 - 8788*E^8*x^3 - 2028*E^8*x^4 - 1014*E^8*x^5 - 104*E^8*x^6 - 52*E^8*
x^7 - 2*E^8*x^8 - E^8*x^9

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fricas [B]  time = 0.48, size = 55, normalized size = 2.39 \begin {gather*} 2 \, x^{2} - {\left (x^{9} + 2 \, x^{8} + 52 \, x^{7} + 104 \, x^{6} + 1014 \, x^{5} + 2028 \, x^{4} + 8788 \, x^{3} + 17576 \, x^{2} + 28561 \, x\right )} e^{8} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9*x^8-16*x^7-364*x^6-624*x^5-5070*x^4-8112*x^3-26364*x^2-35152*x-28561)*exp(2)^4+4*x+5,x, algorith
m="fricas")

[Out]

2*x^2 - (x^9 + 2*x^8 + 52*x^7 + 104*x^6 + 1014*x^5 + 2028*x^4 + 8788*x^3 + 17576*x^2 + 28561*x)*e^8 + 5*x

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giac [B]  time = 0.13, size = 55, normalized size = 2.39 \begin {gather*} 2 \, x^{2} - {\left (x^{9} + 2 \, x^{8} + 52 \, x^{7} + 104 \, x^{6} + 1014 \, x^{5} + 2028 \, x^{4} + 8788 \, x^{3} + 17576 \, x^{2} + 28561 \, x\right )} e^{8} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9*x^8-16*x^7-364*x^6-624*x^5-5070*x^4-8112*x^3-26364*x^2-35152*x-28561)*exp(2)^4+4*x+5,x, algorith
m="giac")

[Out]

2*x^2 - (x^9 + 2*x^8 + 52*x^7 + 104*x^6 + 1014*x^5 + 2028*x^4 + 8788*x^3 + 17576*x^2 + 28561*x)*e^8 + 5*x

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maple [B]  time = 0.04, size = 59, normalized size = 2.57

method	result	size
default	\({\mathrm e}^{8} \left (-x^{9}-2 x^{8}-52 x^{7}-104 x^{6}-1014 x^{5}-2028 x^{4}-8788 x^{3}-17576 x^{2}-28561 x \right )+2 x^{2}+5 x\)	\(59\)
risch	\(-{\mathrm e}^{8} x^{9}-2 \,{\mathrm e}^{8} x^{8}-52 \,{\mathrm e}^{8} x^{7}-104 \,{\mathrm e}^{8} x^{6}-1014 x^{5} {\mathrm e}^{8}-2028 x^{4} {\mathrm e}^{8}-8788 x^{3} {\mathrm e}^{8}-17576 x^{2} {\mathrm e}^{8}-28561 x \,{\mathrm e}^{8}+2 x^{2}+5 x\)	\(71\)
gosper	\(-x \left ({\mathrm e}^{8} x^{8}+2 \,{\mathrm e}^{8} x^{7}+52 \,{\mathrm e}^{8} x^{6}+104 x^{5} {\mathrm e}^{8}+1014 x^{4} {\mathrm e}^{8}+2028 x^{3} {\mathrm e}^{8}+8788 x^{2} {\mathrm e}^{8}+17576 x \,{\mathrm e}^{8}+28561 \,{\mathrm e}^{8}-2 x -5\right )\)	\(84\)
norman	\(\left (-28561 \,{\mathrm e}^{8}+5\right ) x +\left (-17576 \,{\mathrm e}^{8}+2\right ) x^{2}-8788 x^{3} {\mathrm e}^{8}-2028 x^{4} {\mathrm e}^{8}-1014 x^{5} {\mathrm e}^{8}-104 \,{\mathrm e}^{8} x^{6}-52 \,{\mathrm e}^{8} x^{7}-2 \,{\mathrm e}^{8} x^{8}-{\mathrm e}^{8} x^{9}\)	\(87\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-9*x^8-16*x^7-364*x^6-624*x^5-5070*x^4-8112*x^3-26364*x^2-35152*x-28561)*exp(2)^4+4*x+5,x,method=_RETURNV
ERBOSE)

[Out]

exp(2)^4*(-x^9-2*x^8-52*x^7-104*x^6-1014*x^5-2028*x^4-8788*x^3-17576*x^2-28561*x)+2*x^2+5*x

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maxima [B]  time = 0.38, size = 55, normalized size = 2.39 \begin {gather*} 2 \, x^{2} - {\left (x^{9} + 2 \, x^{8} + 52 \, x^{7} + 104 \, x^{6} + 1014 \, x^{5} + 2028 \, x^{4} + 8788 \, x^{3} + 17576 \, x^{2} + 28561 \, x\right )} e^{8} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9*x^8-16*x^7-364*x^6-624*x^5-5070*x^4-8112*x^3-26364*x^2-35152*x-28561)*exp(2)^4+4*x+5,x, algorith
m="maxima")

[Out]

2*x^2 - (x^9 + 2*x^8 + 52*x^7 + 104*x^6 + 1014*x^5 + 2028*x^4 + 8788*x^3 + 17576*x^2 + 28561*x)*e^8 + 5*x

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mupad [B]  time = 0.06, size = 70, normalized size = 3.04 \begin {gather*} -{\mathrm {e}}^8\,x^9-2\,{\mathrm {e}}^8\,x^8-52\,{\mathrm {e}}^8\,x^7-104\,{\mathrm {e}}^8\,x^6-1014\,{\mathrm {e}}^8\,x^5-2028\,{\mathrm {e}}^8\,x^4-8788\,{\mathrm {e}}^8\,x^3+\left (2-17576\,{\mathrm {e}}^8\right )\,x^2+\left (5-28561\,{\mathrm {e}}^8\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x - exp(8)*(35152*x + 26364*x^2 + 8112*x^3 + 5070*x^4 + 624*x^5 + 364*x^6 + 16*x^7 + 9*x^8 + 28561) + 5,
x)

[Out]

- x^2*(17576*exp(8) - 2) - 8788*x^3*exp(8) - 2028*x^4*exp(8) - 1014*x^5*exp(8) - 104*x^6*exp(8) - 52*x^7*exp(8
) - 2*x^8*exp(8) - x^9*exp(8) - x*(28561*exp(8) - 5)

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sympy [B]  time = 0.06, size = 75, normalized size = 3.26 \begin {gather*} - x^{9} e^{8} - 2 x^{8} e^{8} - 52 x^{7} e^{8} - 104 x^{6} e^{8} - 1014 x^{5} e^{8} - 2028 x^{4} e^{8} - 8788 x^{3} e^{8} + x^{2} \left (2 - 17576 e^{8}\right ) + x \left (5 - 28561 e^{8}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-9*x**8-16*x**7-364*x**6-624*x**5-5070*x**4-8112*x**3-26364*x**2-35152*x-28561)*exp(2)**4+4*x+5,x)

[Out]

-x**9*exp(8) - 2*x**8*exp(8) - 52*x**7*exp(8) - 104*x**6*exp(8) - 1014*x**5*exp(8) - 2028*x**4*exp(8) - 8788*x
**3*exp(8) + x**2*(2 - 17576*exp(8)) + x*(5 - 28561*exp(8))

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