3.103.93 \(\int \frac {2048 x^7+e^{32} (1-27 x^2)}{e^{32}} \, dx\)

Optimal. Leaf size=15 \[ x-9 x^3+\frac {256 x^8}{e^{32}} \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {12} \begin {gather*} \frac {256 x^8}{e^{32}}-9 x^3+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2048*x^7 + E^32*(1 - 27*x^2))/E^32,x]

[Out]

x - 9*x^3 + (256*x^8)/E^32

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (2048 x^7+e^{32} \left (1-27 x^2\right )\right ) \, dx}{e^{32}}\\ &=\frac {256 x^8}{e^{32}}+\int \left (1-27 x^2\right ) \, dx\\ &=x-9 x^3+\frac {256 x^8}{e^{32}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} x-9 x^3+\frac {256 x^8}{e^{32}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2048*x^7 + E^32*(1 - 27*x^2))/E^32,x]

[Out]

x - 9*x^3 + (256*x^8)/E^32

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fricas [A]  time = 0.71, size = 22, normalized size = 1.47 \begin {gather*} {\left (256 \, x^{8} - {\left (9 \, x^{3} - x\right )} e^{32}\right )} e^{\left (-32\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-27*x^2+1)*exp(4)^8+2048*x^7)/exp(4)^8,x, algorithm="fricas")

[Out]

(256*x^8 - (9*x^3 - x)*e^32)*e^(-32)

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giac [A]  time = 0.16, size = 22, normalized size = 1.47 \begin {gather*} {\left (256 \, x^{8} - {\left (9 \, x^{3} - x\right )} e^{32}\right )} e^{\left (-32\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-27*x^2+1)*exp(4)^8+2048*x^7)/exp(4)^8,x, algorithm="giac")

[Out]

(256*x^8 - (9*x^3 - x)*e^32)*e^(-32)

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maple [A]  time = 0.03, size = 15, normalized size = 1.00

method	result	size
risch	\(256 x^{8} {\mathrm e}^{-32}+x -9 x^{3}\)	\(15\)
default	\({\mathrm e}^{-32} \left ({\mathrm e}^{32} \left (-9 x^{3}+x \right )+256 x^{8}\right )\)	\(24\)
gosper	\(-x \left (9 \,{\mathrm e}^{32} x^{2}-{\mathrm e}^{32}-256 x^{7}\right ) {\mathrm e}^{-32}\)	\(29\)
norman	\(\left ({\mathrm e}^{28} x +256 \,{\mathrm e}^{-4} x^{8}-9 \,{\mathrm e}^{28} x^{3}\right ) {\mathrm e}^{-28}\)	\(31\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-27*x^2+1)*exp(4)^8+2048*x^7)/exp(4)^8,x,method=_RETURNVERBOSE)

[Out]

256*x^8*exp(-32)+x-9*x^3

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maxima [A]  time = 0.35, size = 22, normalized size = 1.47 \begin {gather*} {\left (256 \, x^{8} - {\left (9 \, x^{3} - x\right )} e^{32}\right )} e^{\left (-32\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-27*x^2+1)*exp(4)^8+2048*x^7)/exp(4)^8,x, algorithm="maxima")

[Out]

(256*x^8 - (9*x^3 - x)*e^32)*e^(-32)

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mupad [B]  time = 0.04, size = 14, normalized size = 0.93 \begin {gather*} 256\,{\mathrm {e}}^{-32}\,x^8-9\,x^3+x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-32)*(exp(32)*(27*x^2 - 1) - 2048*x^7),x)

[Out]

x + 256*x^8*exp(-32) - 9*x^3

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sympy [A]  time = 0.06, size = 14, normalized size = 0.93 \begin {gather*} \frac {256 x^{8}}{e^{32}} - 9 x^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-27*x**2+1)*exp(4)**8+2048*x**7)/exp(4)**8,x)

[Out]

256*x**8*exp(-32) - 9*x**3 + x

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