\(\int \frac {12058624 x^{22}}{e^6} \, dx\) [2178]

Optimal result

Integrand size = 8, antiderivative size = 8 \[ \int \frac {12058624 x^{22}}{e^6} \, dx=\frac {524288 x^{23}}{e^6} \]

[Out]

524288*x^23/exp(3)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {12, 30} \[ \int \frac {12058624 x^{22}}{e^6} \, dx=\frac {524288 x^{23}}{e^6} \]

[In]

Int[(12058624*x^22)/E^6,x]

[Out]

(524288*x^23)/E^6

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}& = \frac {12058624 \int x^{22} \, dx}{e^6} \\ & = \frac {524288 x^{23}}{e^6} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {12058624 x^{22}}{e^6} \, dx=\frac {524288 x^{23}}{e^6} \]

[In]

Integrate[(12058624*x^22)/E^6,x]

[Out]

(524288*x^23)/E^6

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00

method	result	size
risch	\(524288 x^{23} {\mathrm e}^{-6}\)	\(8\)
gosper	\(524288 x^{23} {\mathrm e}^{-6}\)	\(10\)
default	\(524288 x^{23} {\mathrm e}^{-6}\)	\(10\)
norman	\(524288 x^{23} {\mathrm e}^{-6}\)	\(10\)
parallelrisch	\(524288 x^{23} {\mathrm e}^{-6}\)	\(10\)

[In]

int(12058624*x^22/exp(3)^2,x,method=_RETURNVERBOSE)

[Out]

524288*x^23*exp(-6)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {12058624 x^{22}}{e^6} \, dx=524288 \, x^{23} e^{\left (-6\right )} \]

[In]

integrate(12058624*x^22/exp(3)^2,x, algorithm="fricas")

[Out]

524288*x^23*e^(-6)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {12058624 x^{22}}{e^6} \, dx=\frac {524288 x^{23}}{e^{6}} \]

[In]

integrate(12058624*x**22/exp(3)**2,x)

[Out]

524288*x**23*exp(-6)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {12058624 x^{22}}{e^6} \, dx=524288 \, x^{23} e^{\left (-6\right )} \]

[In]

integrate(12058624*x^22/exp(3)^2,x, algorithm="maxima")

[Out]

524288*x^23*e^(-6)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {12058624 x^{22}}{e^6} \, dx=524288 \, x^{23} e^{\left (-6\right )} \]

[In]

integrate(12058624*x^22/exp(3)^2,x, algorithm="giac")

[Out]

524288*x^23*e^(-6)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {12058624 x^{22}}{e^6} \, dx=524288\,x^{23}\,{\mathrm {e}}^{-6} \]

[In]

int(12058624*x^22*exp(-6),x)

[Out]

524288*x^23*exp(-6)