3.66.43 \(\int 144 e^{-10+2 x+6 x^4} x (2+2 x+24 x^4) \, dx\)

Optimal. Leaf size=18 \[ e^{-2+2 \left (-4+x+3 x^4+\log (12 x)\right )} \]

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Rubi [A]  time = 0.04, antiderivative size = 31, normalized size of antiderivative = 1.72, number of steps used = 2, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 2288} \begin {gather*} \frac {144 e^{6 x^4+2 x-10} x \left (12 x^4+x\right )}{12 x^3+1} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[144*E^(-10 + 2*x + 6*x^4)*x*(2 + 2*x + 24*x^4),x]

[Out]

(144*E^(-10 + 2*x + 6*x^4)*x*(x + 12*x^4))/(1 + 12*x^3)

Rule 12

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

Rule 2288

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} &=144 \int e^{-10+2 x+6 x^4} x \left (2+2 x+24 x^4\right ) \, dx\\ &=\frac {144 e^{-10+2 x+6 x^4} x \left (x+12 x^4\right )}{1+12 x^3}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 17, normalized size = 0.94 \begin {gather*} 144 e^{2 \left (-5+x+3 x^4\right )} x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[144*E^(-10 + 2*x + 6*x^4)*x*(2 + 2*x + 24*x^4),x]

[Out]

144*E^(2*(-5 + x + 3*x^4))*x^2

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fricas [A]  time = 0.88, size = 17, normalized size = 0.94 \begin {gather*} e^{\left (6 \, x^{4} + 2 \, x + 2 \, \log \left (12 \, x\right ) - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^4+2*x+2)*exp(2*log(12*x)+6*x^4+2*x-10)/x,x, algorithm="fricas")

[Out]

e^(6*x^4 + 2*x + 2*log(12*x) - 10)

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giac [A]  time = 0.22, size = 17, normalized size = 0.94 \begin {gather*} e^{\left (6 \, x^{4} + 2 \, x + 2 \, \log \left (12 \, x\right ) - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^4+2*x+2)*exp(2*log(12*x)+6*x^4+2*x-10)/x,x, algorithm="giac")

[Out]

e^(6*x^4 + 2*x + 2*log(12*x) - 10)

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maple [A]  time = 0.05, size = 17, normalized size = 0.94

method	result	size
risch	\(144 x^{2} {\mathrm e}^{6 x^{4}+2 x -10}\)	\(17\)
gosper	\({\mathrm e}^{2 \ln \left (12 x \right )+6 x^{4}+2 x -10}\)	\(18\)
norman	\({\mathrm e}^{2 \ln \left (12 x \right )+6 x^{4}+2 x -10}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((24*x^4+2*x+2)*exp(2*ln(12*x)+6*x^4+2*x-10)/x,x,method=_RETURNVERBOSE)

[Out]

144*x^2*exp(6*x^4+2*x-10)

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maxima [A]  time = 0.43, size = 16, normalized size = 0.89 \begin {gather*} 144 \, x^{2} e^{\left (6 \, x^{4} + 2 \, x - 10\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x^4+2*x+2)*exp(2*log(12*x)+6*x^4+2*x-10)/x,x, algorithm="maxima")

[Out]

144*x^2*e^(6*x^4 + 2*x - 10)

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mupad [B]  time = 4.05, size = 17, normalized size = 0.94 \begin {gather*} 144\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-10}\,{\mathrm {e}}^{6\,x^4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x + 2*log(12*x) + 6*x^4 - 10)*(2*x + 24*x^4 + 2))/x,x)

[Out]

144*x^2*exp(2*x)*exp(-10)*exp(6*x^4)

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sympy [A]  time = 0.10, size = 15, normalized size = 0.83 \begin {gather*} 144 x^{2} e^{6 x^{4} + 2 x - 10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((24*x**4+2*x+2)*exp(2*ln(12*x)+6*x**4+2*x-10)/x,x)

[Out]

144*x**2*exp(6*x**4 + 2*x - 10)

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