3.23.11 \(\int \frac {16 e^{24 e^{x^2}} (-32+768 e^{x^2} x^2)}{x^3} \, dx\)

Optimal. Leaf size=14 \[ \frac {256 e^{24 e^{x^2}}}{x^2} \]

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Rubi [A]  time = 0.06, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2288} \begin {gather*} \frac {256 e^{24 e^{x^2}}}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(16*E^(24*E^x^2)*(-32 + 768*E^x^2*x^2))/x^3,x]

[Out]

(256*E^(24*E^x^2))/x^2

Rule 12

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

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} &=16 \int \frac {e^{24 e^{x^2}} \left (-32+768 e^{x^2} x^2\right )}{x^3} \, dx\\ &=\frac {256 e^{24 e^{x^2}}}{x^2}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \frac {256 e^{24 e^{x^2}}}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(16*E^(24*E^x^2)*(-32 + 768*E^x^2*x^2))/x^3,x]

[Out]

(256*E^(24*E^x^2))/x^2

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fricas [A]  time = 0.94, size = 16, normalized size = 1.14 \begin {gather*} 16 \, e^{\left (24 \, e^{\left (x^{2}\right )} - 2 \, \log \left (\frac {1}{4} \, x\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x^2*exp(x^2)-32)/x/exp(log(1/4*x)-12*exp(x^2))^2,x, algorithm="fricas")

[Out]

16*e^(24*e^(x^2) - 2*log(1/4*x))

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giac [A]  time = 0.19, size = 12, normalized size = 0.86 \begin {gather*} \frac {256 \, e^{\left (24 \, e^{\left (x^{2}\right )}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x^2*exp(x^2)-32)/x/exp(log(1/4*x)-12*exp(x^2))^2,x, algorithm="giac")

[Out]

256*e^(24*e^(x^2))/x^2

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maple [A]  time = 0.05, size = 13, normalized size = 0.93

method	result	size
risch	\(\frac {256 \,{\mathrm e}^{24 \,{\mathrm e}^{x^{2}}}}{x^{2}}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((768*x^2*exp(x^2)-32)/x/exp(ln(1/4*x)-12*exp(x^2))^2,x,method=_RETURNVERBOSE)

[Out]

256/x^2*exp(24*exp(x^2))

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maxima [A]  time = 0.54, size = 12, normalized size = 0.86 \begin {gather*} \frac {256 \, e^{\left (24 \, e^{\left (x^{2}\right )}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x^2*exp(x^2)-32)/x/exp(log(1/4*x)-12*exp(x^2))^2,x, algorithm="maxima")

[Out]

256*e^(24*e^(x^2))/x^2

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mupad [B]  time = 1.33, size = 12, normalized size = 0.86 \begin {gather*} \frac {256\,{\mathrm {e}}^{24\,{\mathrm {e}}^{x^2}}}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(24*exp(x^2) - 2*log(x/4))*(768*x^2*exp(x^2) - 32))/x,x)

[Out]

(256*exp(24*exp(x^2)))/x^2

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sympy [A]  time = 0.25, size = 12, normalized size = 0.86 \begin {gather*} \frac {256 e^{24 e^{x^{2}}}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x**2*exp(x**2)-32)/x/exp(ln(1/4*x)-12*exp(x**2))**2,x)

[Out]

256*exp(24*exp(x**2))/x**2

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