∫ − 288e15x2 _____________________________

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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.07, number of steps used = 3, number of rules used = 3, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {12, 28, 261} \begin {gather*} \frac {6 e^{15}}{16 x^3+e^{15}} \end {gather*}

Int[(-288*E^15*x^2)/(E^30 + 32*E^15*x^3 + 256*x^6),x]

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] && !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Int[(u_.)*((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_.), x_Symbol] :> Dist[1/c^p, Int[u*(b/2 + c*x^n)^(2*

p), x], x] /; FreeQ[{a, b, c, n}, x] && EqQ[n2, 2*n] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p]

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[(a + b*x^n)^(p + 1)/(b*n*(p + 1)), x] /; FreeQ

[{a, b, m, n, p}, x] && EqQ[m, n - 1] && NeQ[p, -1]

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (288 e^{15}\right ) \int \frac {x^2}{e^{30}+32 e^{15} x^3+256 x^6} \, dx\right )\\ &=-\left (\left (73728 e^{15}\right ) \int \frac {x^2}{\left (16 e^{15}+256 x^3\right )^2} \, dx\right )\\ &=\frac {6 e^{15}}{e^{15}+16 x^3}\\ \end {aligned} \end {gather*}

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Mathematica [A] time = 0.01, size = 16, normalized size = 1.07 \begin {gather*} \frac {6 e^{15}}{e^{15}+16 x^3} \end {gather*}

Integrate[(-288*E^15*x^2)/(E^30 + 32*E^15*x^3 + 256*x^6),x]

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fricas [A] time = 0.50, size = 14, normalized size = 0.93 \begin {gather*} \frac {6 \, e^{15}}{16 \, x^{3} + e^{15}} \end {gather*}

integrate(-288*x^2*exp(3)^5/(exp(3)^10+32*x^3*exp(3)^5+256*x^6),x, algorithm="fricas")

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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}

integrate(-288*x^2*exp(3)^5/(exp(3)^10+32*x^3*exp(3)^5+256*x^6),x, algorithm="giac")

Exception raised: NotImplementedError >> Unable to parse Giac output: -288*exp(15)/48/sqrt(-exp(15)^2+exp(30))

*atan((16*sageVARx^3+exp(15))/sqrt(-exp(15)^2+exp(30)))

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method	result	size

risch	\(\frac {6 \,{\mathrm e}^{15}}{{\mathrm e}^{15}+16 x^{3}}\)	\(15\)
gosper	\(\frac {6 \,{\mathrm e}^{15}}{{\mathrm e}^{15}+16 x^{3}}\)	\(19\)
norman	\(\frac {6 \,{\mathrm e}^{15}}{{\mathrm e}^{15}+16 x^{3}}\)	\(19\)

int(-288*x^2*exp(3)^5/(exp(3)^10+32*x^3*exp(3)^5+256*x^6),x,method=_RETURNVERBOSE)

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maxima [A] time = 0.36, size = 14, normalized size = 0.93 \begin {gather*} \frac {6 \, e^{15}}{16 \, x^{3} + e^{15}} \end {gather*}

integrate(-288*x^2*exp(3)^5/(exp(3)^10+32*x^3*exp(3)^5+256*x^6),x, algorithm="maxima")

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mupad [B] time = 0.12, size = 14, normalized size = 0.93 \begin {gather*} \frac {6\,{\mathrm {e}}^{15}}{16\,x^3+{\mathrm {e}}^{15}} \end {gather*}

int(-(288*x^2*exp(15))/(exp(30) + 32*x^3*exp(15) + 256*x^6),x)

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sympy [A] time = 0.15, size = 14, normalized size = 0.93 \begin {gather*} \frac {288 e^{15}}{768 x^{3} + 48 e^{15}} \end {gather*}

integrate(-288*x**2*exp(3)**5/(exp(3)**10+32*x**3*exp(3)**5+256*x**6),x)

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3.69.50 \(\int -\frac {288 e^{15} x^2}{e^{30}+32 e^{15} x^3+256 x^6} \, dx\)