\(\int (1+e^{4+3 x+16 x^2+16 x^4} (-3-32 x-64 x^3)) \, dx\) [2755]

   Optimal result
   Rubi [A] (verified)
   Mathematica [A] (verified)
   Maple [A] (verified)
   Fricas [A] (verification not implemented)
   Sympy [A] (verification not implemented)
   Maxima [A] (verification not implemented)
   Giac [A] (verification not implemented)
   Mupad [B] (verification not implemented)

Optimal result

Integrand size = 30, antiderivative size = 23 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=5-e-e^{3 x+\left (2+4 x^2\right )^2}+x \]

[Out]

5-exp(3*x+(4*x^2+2)^2)-exp(1)+x

Rubi [A] (verified)

Time = 0.03 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.033, Rules used = {6838} \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x-e^{16 x^4+16 x^2+3 x+4} \]

[In]

Int[1 + E^(4 + 3*x + 16*x^2 + 16*x^4)*(-3 - 32*x - 64*x^3),x]

[Out]

-E^(4 + 3*x + 16*x^2 + 16*x^4) + x

Rule 6838

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[q*(F^v/Log[F]), x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps \begin{align*} \text {integral}& = x+\int e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right ) \, dx \\ & = -e^{4+3 x+16 x^2+16 x^4}+x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.04 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=-e^{4+3 x+16 x^2+16 x^4}+x \]

[In]

Integrate[1 + E^(4 + 3*x + 16*x^2 + 16*x^4)*(-3 - 32*x - 64*x^3),x]

[Out]

-E^(4 + 3*x + 16*x^2 + 16*x^4) + x

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91

method result size
default \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) \(21\)
norman \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) \(21\)
risch \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) \(21\)
parallelrisch \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) \(21\)
parts \(x -{\mathrm e}^{16 x^{4}+16 x^{2}+3 x +4}\) \(21\)

[In]

int((-64*x^3-32*x-3)*exp(16*x^4+16*x^2+3*x+4)+1,x,method=_RETURNVERBOSE)

[Out]

x-exp(16*x^4+16*x^2+3*x+4)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \]

[In]

integrate((-64*x^3-32*x-3)*exp(16*x^4+16*x^2+3*x+4)+1,x, algorithm="fricas")

[Out]

x - e^(16*x^4 + 16*x^2 + 3*x + 4)

Sympy [A] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.74 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{16 x^{4} + 16 x^{2} + 3 x + 4} \]

[In]

integrate((-64*x**3-32*x-3)*exp(16*x**4+16*x**2+3*x+4)+1,x)

[Out]

x - exp(16*x**4 + 16*x**2 + 3*x + 4)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \]

[In]

integrate((-64*x^3-32*x-3)*exp(16*x^4+16*x^2+3*x+4)+1,x, algorithm="maxima")

[Out]

x - e^(16*x^4 + 16*x^2 + 3*x + 4)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x - e^{\left (16 \, x^{4} + 16 \, x^{2} + 3 \, x + 4\right )} \]

[In]

integrate((-64*x^3-32*x-3)*exp(16*x^4+16*x^2+3*x+4)+1,x, algorithm="giac")

[Out]

x - e^(16*x^4 + 16*x^2 + 3*x + 4)

Mupad [B] (verification not implemented)

Time = 9.42 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \left (1+e^{4+3 x+16 x^2+16 x^4} \left (-3-32 x-64 x^3\right )\right ) \, dx=x-{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^4\,{\mathrm {e}}^{16\,x^2}\,{\mathrm {e}}^{16\,x^4} \]

[In]

int(1 - exp(3*x + 16*x^2 + 16*x^4 + 4)*(32*x + 64*x^3 + 3),x)

[Out]

x - exp(3*x)*exp(4)*exp(16*x^2)*exp(16*x^4)