\(\int -\frac {e^4}{x^3} \, dx\) [6999]

Optimal result

Integrand size = 8, antiderivative size = 17 \[ \int -\frac {e^4}{x^3} \, dx=2 \left (\frac {e^4}{4 x^2}-11 \log (3)\right ) \]

[Out]

1/2*exp(4)/x^2-22*ln(3)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^4}{2 x^2} \]

[In]

Int[-(E^4/x^3),x]

[Out]

E^4/(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 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps \begin{align*} \text {integral}& = -\left (e^4 \int \frac {1}{x^3} \, dx\right ) \\ & = \frac {e^4}{2 x^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^4}{2 x^2} \]

[In]

Integrate[-(E^4/x^3),x]

[Out]

E^4/(2*x^2)

Maple [A] (verified)

Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47

method	result	size
gosper	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)
default	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)
norman	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)
risch	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)
parallelrisch	\(\frac {{\mathrm e}^{4}}{2 x^{2}}\)	\(8\)

[In]

int(-exp(4)/x^3,x,method=_RETURNVERBOSE)

[Out]

1/2*exp(4)/x^2

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 \, x^{2}} \]

[In]

integrate(-exp(4)/x^3,x, algorithm="fricas")

[Out]

1/2*e^4/x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 x^{2}} \]

[In]

integrate(-exp(4)/x**3,x)

[Out]

exp(4)/(2*x**2)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 \, x^{2}} \]

[In]

integrate(-exp(4)/x^3,x, algorithm="maxima")

[Out]

1/2*e^4/x^2

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {e^{4}}{2 \, x^{2}} \]

[In]

integrate(-exp(4)/x^3,x, algorithm="giac")

[Out]

1/2*e^4/x^2

Mupad [B] (verification not implemented)

Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.41 \[ \int -\frac {e^4}{x^3} \, dx=\frac {{\mathrm {e}}^4}{2\,x^2} \]

[In]

int(-exp(4)/x^3,x)

[Out]

exp(4)/(2*x^2)