\(\int (-2+e^{16} x) \, dx\) [3397]

Optimal result

Integrand size = 7, antiderivative size = 19 \[ \int \left (-2+e^{16} x\right ) \, dx=1+2 \left (9-x+\frac {e^{16} x^2}{4}\right ) \]

[Out]

19-2*x+1/2*x^2*exp(16)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-2+e^{16} x\right ) \, dx=\frac {e^{16} x^2}{2}-2 x \]

[In]

Int[-2 + E^16*x,x]

[Out]

-2*x + (E^16*x^2)/2

Rubi steps \begin{align*} \text {integral}& = -2 x+\frac {e^{16} x^2}{2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int \left (-2+e^{16} x\right ) \, dx=-2 x+\frac {e^{16} x^2}{2} \]

[In]

Integrate[-2 + E^16*x,x]

[Out]

-2*x + (E^16*x^2)/2

Maple [A] (verified)

Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63

method	result	size
gosper	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
default	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
norman	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
risch	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
parallelrisch	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)
parts	\(\frac {x^{2} {\mathrm e}^{16}}{2}-2 x\)	\(12\)

[In]

int(x*exp(16)-2,x,method=_RETURNVERBOSE)

[Out]

1/2*x^2*exp(16)-2*x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \left (-2+e^{16} x\right ) \, dx=\frac {1}{2} \, x^{2} e^{16} - 2 \, x \]

[In]

integrate(x*exp(16)-2,x, algorithm="fricas")

[Out]

1/2*x^2*e^16 - 2*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53 \[ \int \left (-2+e^{16} x\right ) \, dx=\frac {x^{2} e^{16}}{2} - 2 x \]

[In]

integrate(x*exp(16)-2,x)

[Out]

x**2*exp(16)/2 - 2*x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \left (-2+e^{16} x\right ) \, dx=\frac {1}{2} \, x^{2} e^{16} - 2 \, x \]

[In]

integrate(x*exp(16)-2,x, algorithm="maxima")

[Out]

1/2*x^2*e^16 - 2*x

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \left (-2+e^{16} x\right ) \, dx=\frac {1}{2} \, x^{2} e^{16} - 2 \, x \]

[In]

integrate(x*exp(16)-2,x, algorithm="giac")

[Out]

1/2*x^2*e^16 - 2*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.47 \[ \int \left (-2+e^{16} x\right ) \, dx=\frac {x\,\left (x\,{\mathrm {e}}^{16}-4\right )}{2} \]

[In]

int(x*exp(16) - 2,x)

[Out]

(x*(x*exp(16) - 4))/2