3.96.69 \(\int \frac {e^{\frac {3 x^2-3 \log (x^2)}{x^6}} (-6-12 x^2+18 \log (x^2))}{x^7} \, dx\)

Optimal. Leaf size=17 \[ e^{\frac {3 \left (x^2-\log \left (x^2\right )\right )}{x^6}} \]

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Rubi [A]  time = 0.24, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6706} \begin {gather*} e^{\frac {3}{x^4}} \left (x^2\right )^{-\frac {3}{x^6}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((3*x^2 - 3*Log[x^2])/x^6)*(-6 - 12*x^2 + 18*Log[x^2]))/x^7,x]

[Out]

E^(3/x^4)/(x^2)^(3/x^6)

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^{\frac {3}{x^4}} \left (x^2\right )^{-\frac {3}{x^6}}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 17, normalized size = 1.00 \begin {gather*} e^{\frac {3}{x^4}} \left (x^2\right )^{-\frac {3}{x^6}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((3*x^2 - 3*Log[x^2])/x^6)*(-6 - 12*x^2 + 18*Log[x^2]))/x^7,x]

[Out]

E^(3/x^4)/(x^2)^(3/x^6)

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fricas [A]  time = 0.56, size = 16, normalized size = 0.94 \begin {gather*} e^{\left (\frac {3 \, {\left (x^{2} - \log \left (x^{2}\right )\right )}}{x^{6}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((18*log(x^2)-12*x^2-6)*exp((-3*log(x^2)+3*x^2)/x^6)/x^7,x, algorithm="fricas")

[Out]

e^(3*(x^2 - log(x^2))/x^6)

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giac [A]  time = 0.15, size = 16, normalized size = 0.94 \begin {gather*} e^{\left (\frac {3}{x^{4}} - \frac {3 \, \log \left (x^{2}\right )}{x^{6}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((18*log(x^2)-12*x^2-6)*exp((-3*log(x^2)+3*x^2)/x^6)/x^7,x, algorithm="giac")

[Out]

e^(3/x^4 - 3*log(x^2)/x^6)

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maple [A]  time = 0.06, size = 17, normalized size = 1.00

method	result	size
risch	\(\left (x^{2}\right )^{-\frac {3}{x^{6}}} {\mathrm e}^{\frac {3}{x^{4}}}\)	\(17\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((18*ln(x^2)-12*x^2-6)*exp((-3*ln(x^2)+3*x^2)/x^6)/x^7,x,method=_RETURNVERBOSE)

[Out]

(x^2)^(-3/x^6)*exp(3/x^4)

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maxima [A]  time = 0.45, size = 14, normalized size = 0.82 \begin {gather*} e^{\left (\frac {3}{x^{4}} - \frac {6 \, \log \relax (x)}{x^{6}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((18*log(x^2)-12*x^2-6)*exp((-3*log(x^2)+3*x^2)/x^6)/x^7,x, algorithm="maxima")

[Out]

e^(3/x^4 - 6*log(x)/x^6)

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mupad [B]  time = 7.92, size = 18, normalized size = 1.06 \begin {gather*} \frac {{\mathrm {e}}^{\frac {3}{x^4}}}{{\left (x^2\right )}^{\frac {3}{x^6}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-(3*log(x^2) - 3*x^2)/x^6)*(12*x^2 - 18*log(x^2) + 6))/x^7,x)

[Out]

exp(3/x^4)/(x^2)^(3/x^6)

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sympy [A]  time = 0.31, size = 15, normalized size = 0.88 \begin {gather*} e^{\frac {3 x^{2} - 3 \log {\left (x^{2} \right )}}{x^{6}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((18*ln(x**2)-12*x**2-6)*exp((-3*ln(x**2)+3*x**2)/x**6)/x**7,x)

[Out]

exp((3*x**2 - 3*log(x**2))/x**6)

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