\(\int (-60-e^x+178 x-72 x^2+64 x^3) \, dx\) [8001]

Optimal result

Integrand size = 20, antiderivative size = 21 \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=-e^x+\left (6+x+4 \left (1-x+x^2\right )\right )^2 \]

[Out]

(4*x^2-3*x+10)^2-exp(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2225} \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=16 x^4-24 x^3+89 x^2-60 x-e^x \]

[In]

Int[-60 - E^x + 178*x - 72*x^2 + 64*x^3,x]

[Out]

-E^x - 60*x + 89*x^2 - 24*x^3 + 16*x^4

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = -60 x+89 x^2-24 x^3+16 x^4-\int e^x \, dx \\ & = -e^x-60 x+89 x^2-24 x^3+16 x^4 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=-e^x-60 x+89 x^2-24 x^3+16 x^4 \]

[In]

Integrate[-60 - E^x + 178*x - 72*x^2 + 64*x^3,x]

[Out]

-E^x - 60*x + 89*x^2 - 24*x^3 + 16*x^4

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14

method	result	size
default	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)
norman	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)
risch	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)
parallelrisch	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)
parts	\(16 x^{4}-24 x^{3}+89 x^{2}-60 x -{\mathrm e}^{x}\)	\(24\)

[In]

int(-exp(x)+64*x^3-72*x^2+178*x-60,x,method=_RETURNVERBOSE)

[Out]

16*x^4-24*x^3+89*x^2-60*x-exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \]

[In]

integrate(-exp(x)+64*x^3-72*x^2+178*x-60,x, algorithm="fricas")

[Out]

16*x^4 - 24*x^3 + 89*x^2 - 60*x - e^x

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.95 \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=16 x^{4} - 24 x^{3} + 89 x^{2} - 60 x - e^{x} \]

[In]

integrate(-exp(x)+64*x**3-72*x**2+178*x-60,x)

[Out]

16*x**4 - 24*x**3 + 89*x**2 - 60*x - exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \]

[In]

integrate(-exp(x)+64*x^3-72*x^2+178*x-60,x, algorithm="maxima")

[Out]

16*x^4 - 24*x^3 + 89*x^2 - 60*x - e^x

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=16 \, x^{4} - 24 \, x^{3} + 89 \, x^{2} - 60 \, x - e^{x} \]

[In]

integrate(-exp(x)+64*x^3-72*x^2+178*x-60,x, algorithm="giac")

[Out]

16*x^4 - 24*x^3 + 89*x^2 - 60*x - e^x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.10 \[ \int \left (-60-e^x+178 x-72 x^2+64 x^3\right ) \, dx=89\,x^2-{\mathrm {e}}^x-60\,x-24\,x^3+16\,x^4 \]

[In]

int(178*x - exp(x) - 72*x^2 + 64*x^3 - 60,x)

[Out]

89*x^2 - exp(x) - 60*x - 24*x^3 + 16*x^4