3.75.57 \(\int \frac {e^{64 x^3} (-4+768 x^3)}{x^2} \, dx\) [7457]

Optimal. Leaf size=15 \[ 4 \left (2+\frac {e^{64 x^3}}{x}\right ) \]

[Out]

8+4*exp(64*x^3)/x

________________________________________________________________________________________

Rubi [A]
time = 0.04, antiderivative size = 12, normalized size of antiderivative = 0.80, number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {2326} \begin {gather*} \frac {4 e^{64 x^3}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^(64*x^3)*(-4 + 768*x^3))/x^2,x]

[Out]

(4*E^(64*x^3))/x

Rule 2326

Int[(y_.)*(F_)^(u_)*((v_) + (w_)), x_Symbol] :> With[{z = v*(y/(Log[F]*D[u, x]))}, Simp[F^u*z, x] /; EqQ[D[z,
x], w*y]] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{64 x^3}}{x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]
time = 0.06, size = 12, normalized size = 0.80 \begin {gather*} \frac {4 e^{64 x^3}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(64*x^3)*(-4 + 768*x^3))/x^2,x]

[Out]

(4*E^(64*x^3))/x

________________________________________________________________________________________

Maple [A]
time = 0.24, size = 12, normalized size = 0.80

method	result	size
gosper	\(\frac {4 \,{\mathrm e}^{64 x^{3}}}{x}\)	\(12\)
norman	\(\frac {4 \,{\mathrm e}^{64 x^{3}}}{x}\)	\(12\)
risch	\(\frac {4 \,{\mathrm e}^{64 x^{3}}}{x}\)	\(12\)
meijerg	\(-16 \left (-1\right )^{\frac {1}{3}} \left (\frac {x^{2} \left (-1\right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )}{\left (-x^{3}\right )^{\frac {2}{3}}}-\frac {\left (-1\right )^{\frac {2}{3}} x^{2} \Gamma \left (\frac {2}{3}, -64 x^{3}\right )}{\left (-x^{3}\right )^{\frac {2}{3}}}\right )-\frac {16 \left (-1\right )^{\frac {1}{3}} \left (-\frac {3 x^{2} \left (-1\right )^{\frac {2}{3}} \Gamma \left (\frac {2}{3}\right )}{\left (-x^{3}\right )^{\frac {2}{3}}}+\frac {3 \left (-1\right )^{\frac {2}{3}} {\mathrm e}^{64 x^{3}}}{4 x}+\frac {3 \left (-1\right )^{\frac {2}{3}} x^{2} \Gamma \left (\frac {2}{3}, -64 x^{3}\right )}{\left (-x^{3}\right )^{\frac {2}{3}}}\right )}{3}\)	\(105\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((768*x^3-4)*exp(64*x^3)/x^2,x,method=_RETURNVERBOSE)

[Out]

4*exp(64*x^3)/x

________________________________________________________________________________________

Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order 3.
time = 0.31, size = 39, normalized size = 2.60 \begin {gather*} -\frac {16 \, x^{2} \Gamma \left (\frac {2}{3}, -64 \, x^{3}\right )}{\left (-x^{3}\right )^{\frac {2}{3}}} + \frac {16 \, \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (-\frac {1}{3}, -64 \, x^{3}\right )}{3 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x^3-4)*exp(64*x^3)/x^2,x, algorithm="maxima")

[Out]

-16*x^2*gamma(2/3, -64*x^3)/(-x^3)^(2/3) + 16/3*(-x^3)^(1/3)*gamma(-1/3, -64*x^3)/x

________________________________________________________________________________________

Fricas [A]
time = 0.39, size = 11, normalized size = 0.73 \begin {gather*} \frac {4 \, e^{\left (64 \, x^{3}\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x^3-4)*exp(64*x^3)/x^2,x, algorithm="fricas")

[Out]

4*e^(64*x^3)/x

________________________________________________________________________________________

Sympy [A]
time = 0.03, size = 8, normalized size = 0.53 \begin {gather*} \frac {4 e^{64 x^{3}}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x**3-4)*exp(64*x**3)/x**2,x)

[Out]

4*exp(64*x**3)/x

________________________________________________________________________________________

Giac [A]
time = 0.41, size = 11, normalized size = 0.73 \begin {gather*} \frac {4 \, e^{\left (64 \, x^{3}\right )}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((768*x^3-4)*exp(64*x^3)/x^2,x, algorithm="giac")

[Out]

4*e^(64*x^3)/x

________________________________________________________________________________________

Mupad [B]
time = 0.05, size = 11, normalized size = 0.73 \begin {gather*} \frac {4\,{\mathrm {e}}^{64\,x^3}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(64*x^3)*(768*x^3 - 4))/x^2,x)

[Out]

(4*exp(64*x^3))/x

________________________________________________________________________________________