3.34.11 \(\int \frac {-1536-15 e^{12}}{256 x^2} \, dx\)

Optimal. Leaf size=14 \[ \frac {3 \left (2+\frac {5 e^{12}}{256}\right )}{x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 30} \begin {gather*} \frac {3 \left (512+5 e^{12}\right )}{256 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1536 - 15*E^12)/(256*x^2),x]

[Out]

(3*(512 + 5*E^12))/(256*x)

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 {gather*} \begin {aligned} \text {integral} &=-\left (\frac {1}{256} \left (3 \left (512+5 e^{12}\right )\right ) \int \frac {1}{x^2} \, dx\right )\\ &=\frac {3 \left (512+5 e^{12}\right )}{256 x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} \frac {3 \left (512+5 e^{12}\right )}{256 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1536 - 15*E^12)/(256*x^2),x]

[Out]

(3*(512 + 5*E^12))/(256*x)

________________________________________________________________________________________

fricas [A]  time = 0.44, size = 11, normalized size = 0.79 \begin {gather*} \frac {3 \, {\left (5 \, e^{12} + 512\right )}}{256 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/256*(-15*exp(4)^3-1536)/x^2,x, algorithm="fricas")

[Out]

3/256*(5*e^12 + 512)/x

________________________________________________________________________________________

giac [A]  time = 0.20, size = 11, normalized size = 0.79 \begin {gather*} \frac {3 \, {\left (5 \, e^{12} + 512\right )}}{256 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/256*(-15*exp(4)^3-1536)/x^2,x, algorithm="giac")

[Out]

3/256*(5*e^12 + 512)/x

________________________________________________________________________________________

maple [A]  time = 0.02, size = 13, normalized size = 0.93

method	result	size
norman	\(\frac {\frac {15 \,{\mathrm e}^{12}}{256}+6}{x}\)	\(13\)
gosper	\(\frac {\frac {15 \,{\mathrm e}^{12}}{256}+6}{x}\)	\(14\)
default	\(-\frac {-\frac {15 \,{\mathrm e}^{12}}{256}-6}{x}\)	\(14\)
risch	\(\frac {15 \,{\mathrm e}^{12}}{256 x}+\frac {6}{x}\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/256*(-15*exp(4)^3-1536)/x^2,x,method=_RETURNVERBOSE)

[Out]

(15/256*exp(4)^3+6)/x

________________________________________________________________________________________

maxima [A]  time = 0.51, size = 11, normalized size = 0.79 \begin {gather*} \frac {3 \, {\left (5 \, e^{12} + 512\right )}}{256 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/256*(-15*exp(4)^3-1536)/x^2,x, algorithm="maxima")

[Out]

3/256*(5*e^12 + 512)/x

________________________________________________________________________________________

mupad [B]  time = 0.03, size = 10, normalized size = 0.71 \begin {gather*} \frac {\frac {15\,{\mathrm {e}}^{12}}{256}+6}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((15*exp(12))/256 + 6)/x^2,x)

[Out]

((15*exp(12))/256 + 6)/x

________________________________________________________________________________________

sympy [A]  time = 0.06, size = 12, normalized size = 0.86 \begin {gather*} - \frac {- \frac {15 e^{12}}{256} - 6}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/256*(-15*exp(4)**3-1536)/x**2,x)

[Out]

-(-15*exp(12)/256 - 6)/x

________________________________________________________________________________________