3.37.69 \(\int (240 x^4+48 x^5-64 x^7+e^{e^x} (-64 x^3-16 e^x x^4)) \, dx\)

Optimal. Leaf size=29 \[ 16 x^4 \left (-e^{e^x}+3 x+\frac {1}{2} \left (x^2-x^4\right )\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 26, normalized size of antiderivative = 0.90, number of steps used = 2, number of rules used = 1, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {2288} \begin {gather*} -8 x^8+8 x^6+48 x^5-16 e^{e^x} x^4 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[240*x^4 + 48*x^5 - 64*x^7 + E^E^x*(-64*x^3 - 16*E^x*x^4),x]

[Out]

-16*E^E^x*x^4 + 48*x^5 + 8*x^6 - 8*x^8

Rule 2288

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = (v*y)/(Log[F]*D[u, x])}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=48 x^5+8 x^6-8 x^8+\int e^{e^x} \left (-64 x^3-16 e^x x^4\right ) \, dx\\ &=-16 e^{e^x} x^4+48 x^5+8 x^6-8 x^8\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 23, normalized size = 0.79 \begin {gather*} -8 x^4 \left (2 e^{e^x}+x \left (-6-x+x^3\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[240*x^4 + 48*x^5 - 64*x^7 + E^E^x*(-64*x^3 - 16*E^x*x^4),x]

[Out]

-8*x^4*(2*E^E^x + x*(-6 - x + x^3))

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fricas [A]  time = 0.75, size = 24, normalized size = 0.83 \begin {gather*} -8 \, x^{8} + 8 \, x^{6} + 48 \, x^{5} - 16 \, x^{4} e^{\left (e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*exp(x)*x^4-64*x^3)*exp(exp(x))-64*x^7+48*x^5+240*x^4,x, algorithm="fricas")

[Out]

-8*x^8 + 8*x^6 + 48*x^5 - 16*x^4*e^(e^x)

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giac [A]  time = 0.26, size = 24, normalized size = 0.83 \begin {gather*} -8 \, x^{8} + 8 \, x^{6} + 48 \, x^{5} - 16 \, x^{4} e^{\left (e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*exp(x)*x^4-64*x^3)*exp(exp(x))-64*x^7+48*x^5+240*x^4,x, algorithm="giac")

[Out]

-8*x^8 + 8*x^6 + 48*x^5 - 16*x^4*e^(e^x)

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maple [A]  time = 0.04, size = 25, normalized size = 0.86

method	result	size
default	\(-16 x^{4} {\mathrm e}^{{\mathrm e}^{x}}+48 x^{5}+8 x^{6}-8 x^{8}\)	\(25\)
norman	\(-16 x^{4} {\mathrm e}^{{\mathrm e}^{x}}+48 x^{5}+8 x^{6}-8 x^{8}\)	\(25\)
risch	\(-16 x^{4} {\mathrm e}^{{\mathrm e}^{x}}+48 x^{5}+8 x^{6}-8 x^{8}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-16*exp(x)*x^4-64*x^3)*exp(exp(x))-64*x^7+48*x^5+240*x^4,x,method=_RETURNVERBOSE)

[Out]

-16*x^4*exp(exp(x))+48*x^5+8*x^6-8*x^8

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maxima [A]  time = 0.36, size = 24, normalized size = 0.83 \begin {gather*} -8 \, x^{8} + 8 \, x^{6} + 48 \, x^{5} - 16 \, x^{4} e^{\left (e^{x}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*exp(x)*x^4-64*x^3)*exp(exp(x))-64*x^7+48*x^5+240*x^4,x, algorithm="maxima")

[Out]

-8*x^8 + 8*x^6 + 48*x^5 - 16*x^4*e^(e^x)

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mupad [B]  time = 2.13, size = 22, normalized size = 0.76 \begin {gather*} 8\,x^4\,\left (6\,x-2\,{\mathrm {e}}^{{\mathrm {e}}^x}+x^2-x^4\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(240*x^4 - exp(exp(x))*(16*x^4*exp(x) + 64*x^3) + 48*x^5 - 64*x^7,x)

[Out]

8*x^4*(6*x - 2*exp(exp(x)) + x^2 - x^4)

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sympy [A]  time = 0.15, size = 24, normalized size = 0.83 \begin {gather*} - 8 x^{8} + 8 x^{6} + 48 x^{5} - 16 x^{4} e^{e^{x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-16*exp(x)*x**4-64*x**3)*exp(exp(x))-64*x**7+48*x**5+240*x**4,x)

[Out]

-8*x**8 + 8*x**6 + 48*x**5 - 16*x**4*exp(exp(x))

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