3.51.90 \(\int e^{6401 x-6400 x^3+2400 x^5-400 x^7+25 x^9} (6401-19200 x^2+12000 x^4-2800 x^6+225 x^8) \, dx\)

Optimal. Leaf size=14 \[ e^{x+25 x \left (-4+x^2\right )^4} \]

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Rubi [A]  time = 0.12, antiderivative size = 26, normalized size of antiderivative = 1.86, number of steps used = 1, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6706} \begin {gather*} e^{25 x^9-400 x^7+2400 x^5-6400 x^3+6401 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(6401*x - 6400*x^3 + 2400*x^5 - 400*x^7 + 25*x^9)*(6401 - 19200*x^2 + 12000*x^4 - 2800*x^6 + 225*x^8),x]

[Out]

E^(6401*x - 6400*x^3 + 2400*x^5 - 400*x^7 + 25*x^9)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{6401 x-6400 x^3+2400 x^5-400 x^7+25 x^9}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.15, size = 26, normalized size = 1.86 \begin {gather*} e^{6401 x-6400 x^3+2400 x^5-400 x^7+25 x^9} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(6401*x - 6400*x^3 + 2400*x^5 - 400*x^7 + 25*x^9)*(6401 - 19200*x^2 + 12000*x^4 - 2800*x^6 + 225*x
^8),x]

[Out]

E^(6401*x - 6400*x^3 + 2400*x^5 - 400*x^7 + 25*x^9)

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fricas [A]  time = 0.61, size = 25, normalized size = 1.79 \begin {gather*} e^{\left (25 \, x^{9} - 400 \, x^{7} + 2400 \, x^{5} - 6400 \, x^{3} + 6401 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((225*x^8-2800*x^6+12000*x^4-19200*x^2+6401)*exp(25*x^9-400*x^7+2400*x^5-6400*x^3+6401*x),x, algorith
m="fricas")

[Out]

e^(25*x^9 - 400*x^7 + 2400*x^5 - 6400*x^3 + 6401*x)

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giac [A]  time = 0.20, size = 25, normalized size = 1.79 \begin {gather*} e^{\left (25 \, x^{9} - 400 \, x^{7} + 2400 \, x^{5} - 6400 \, x^{3} + 6401 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((225*x^8-2800*x^6+12000*x^4-19200*x^2+6401)*exp(25*x^9-400*x^7+2400*x^5-6400*x^3+6401*x),x, algorith
m="giac")

[Out]

e^(25*x^9 - 400*x^7 + 2400*x^5 - 6400*x^3 + 6401*x)

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maple [A]  time = 0.04, size = 26, normalized size = 1.86

method	result	size
gosper	\({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\)	\(26\)
derivativedivides	\({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\)	\(26\)
default	\({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\)	\(26\)
norman	\({\mathrm e}^{25 x^{9}-400 x^{7}+2400 x^{5}-6400 x^{3}+6401 x}\)	\(26\)
risch	\({\mathrm e}^{x \left (25 x^{8}-400 x^{6}+2400 x^{4}-6400 x^{2}+6401\right )}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((225*x^8-2800*x^6+12000*x^4-19200*x^2+6401)*exp(25*x^9-400*x^7+2400*x^5-6400*x^3+6401*x),x,method=_RETURNV
ERBOSE)

[Out]

exp(25*x^9-400*x^7+2400*x^5-6400*x^3+6401*x)

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maxima [A]  time = 0.34, size = 25, normalized size = 1.79 \begin {gather*} e^{\left (25 \, x^{9} - 400 \, x^{7} + 2400 \, x^{5} - 6400 \, x^{3} + 6401 \, x\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((225*x^8-2800*x^6+12000*x^4-19200*x^2+6401)*exp(25*x^9-400*x^7+2400*x^5-6400*x^3+6401*x),x, algorith
m="maxima")

[Out]

e^(25*x^9 - 400*x^7 + 2400*x^5 - 6400*x^3 + 6401*x)

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mupad [B]  time = 0.09, size = 29, normalized size = 2.07 \begin {gather*} {\mathrm {e}}^{6401\,x}\,{\mathrm {e}}^{25\,x^9}\,{\mathrm {e}}^{-400\,x^7}\,{\mathrm {e}}^{2400\,x^5}\,{\mathrm {e}}^{-6400\,x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(6401*x - 6400*x^3 + 2400*x^5 - 400*x^7 + 25*x^9)*(12000*x^4 - 19200*x^2 - 2800*x^6 + 225*x^8 + 6401),x
)

[Out]

exp(6401*x)*exp(25*x^9)*exp(-400*x^7)*exp(2400*x^5)*exp(-6400*x^3)

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sympy [A]  time = 0.13, size = 24, normalized size = 1.71 \begin {gather*} e^{25 x^{9} - 400 x^{7} + 2400 x^{5} - 6400 x^{3} + 6401 x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((225*x**8-2800*x**6+12000*x**4-19200*x**2+6401)*exp(25*x**9-400*x**7+2400*x**5-6400*x**3+6401*x),x)

[Out]

exp(25*x**9 - 400*x**7 + 2400*x**5 - 6400*x**3 + 6401*x)

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