\(\int \frac {e^{\frac {3 x^2-3 \log (x^2)}{x^6}} (-6-12 x^2+18 \log (x^2))}{x^7} \, dx\) [9569]

Optimal result

Integrand size = 35, antiderivative size = 17 \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=e^{\frac {3 \left (x^2-\log \left (x^2\right )\right )}{x^6}} \]

[Out]

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

Rubi [A] (verified)

Time = 0.15 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6838} \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=e^{\frac {3}{x^4}} \left (x^2\right )^{-\frac {3}{x^6}} \]

[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 6838

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{align*} \text {integral}& = e^{\frac {3}{x^4}} \left (x^2\right )^{-\frac {3}{x^6}} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=e^{\frac {3}{x^4}} \left (x^2\right )^{-\frac {3}{x^6}} \]

[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)

Maple [A] (verified)

Time = 0.44 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00

method	result	size
risch	\(\left (x^{2}\right )^{-\frac {3}{x^{6}}} {\mathrm e}^{\frac {3}{x^{4}}}\)	\(17\)
parallelrisch	\({\mathrm e}^{-\frac {3 \left (\ln \left (x^{2}\right )-x^{2}\right )}{x^{6}}}\)	\(17\)
default	\({\mathrm e}^{\frac {-3 \ln \left (x^{2}\right )+3 x^{2}}{x^{6}}}\)	\(18\)

[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)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=e^{\left (\frac {3 \, {\left (x^{2} - \log \left (x^{2}\right )\right )}}{x^{6}}\right )} \]

[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)

Sympy [A] (verification not implemented)

Time = 0.13 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.88 \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=e^{\frac {3 x^{2} - 3 \log {\left (x^{2} \right )}}{x^{6}}} \]

[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)

Maxima [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.82 \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=e^{\left (\frac {3}{x^{4}} - \frac {6 \, \log \left (x\right )}{x^{6}}\right )} \]

[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)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.94 \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=e^{\left (\frac {3}{x^{4}} - \frac {3 \, \log \left (x^{2}\right )}{x^{6}}\right )} \]

[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)

Mupad [B] (verification not implemented)

Time = 14.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06 \[ \int \frac {e^{\frac {3 x^2-3 \log \left (x^2\right )}{x^6}} \left (-6-12 x^2+18 \log \left (x^2\right )\right )}{x^7} \, dx=\frac {{\mathrm {e}}^{\frac {3}{x^4}}}{{\left (x^2\right )}^{\frac {3}{x^6}}} \]

[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)