\(\int \frac {10+e (-1+2 x)}{e} \, dx\) [389]

Optimal result

Integrand size = 13, antiderivative size = 19 \[ \int \frac {10+e (-1+2 x)}{e} \, dx=-10+\frac {5}{e^3}-x+\left (\frac {5}{e}+x\right )^2 \]

[Out]

5/exp(3)-10-x+(x+5/exp(1))^2

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12} \[ \int \frac {10+e (-1+2 x)}{e} \, dx=\frac {1}{4} (1-2 x)^2+\frac {10 x}{e} \]

[In]

Int[(10 + E*(-1 + 2*x))/E,x]

[Out]

(1 - 2*x)^2/4 + (10*x)/E

Rule 12

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

Rubi steps \begin{align*} \text {integral}& = \frac {\int (10+e (-1+2 x)) \, dx}{e} \\ & = \frac {1}{4} (1-2 x)^2+\frac {10 x}{e} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68 \[ \int \frac {10+e (-1+2 x)}{e} \, dx=-x+\frac {10 x}{e}+x^2 \]

[In]

Integrate[(10 + E*(-1 + 2*x))/E,x]

[Out]

-x + (10*x)/E + x^2

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68

method	result	size
risch	\(x^{2}-x +10 \,{\mathrm e}^{-1} x\)	\(13\)
norman	\(x^{2}-{\mathrm e}^{-1} \left ({\mathrm e}-10\right ) x\)	\(16\)
gosper	\(x \left (x \,{\mathrm e}-{\mathrm e}+10\right ) {\mathrm e}^{-1}\)	\(17\)
parallelrisch	\({\mathrm e}^{-1} \left ({\mathrm e} \left (x^{2}-x \right )+10 x \right )\)	\(20\)
default	\({\mathrm e}^{-1} \left (x^{2} {\mathrm e}-x \,{\mathrm e}+10 x \right )\)	\(21\)

[In]

int(((-1+2*x)*exp(1)+10)/exp(1),x,method=_RETURNVERBOSE)

[Out]

x^2-x+10*exp(-1)*x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {10+e (-1+2 x)}{e} \, dx={\left ({\left (x^{2} - x\right )} e + 10 \, x\right )} e^{\left (-1\right )} \]

[In]

integrate(((-1+2*x)*exp(1)+10)/exp(1),x, algorithm="fricas")

[Out]

((x^2 - x)*e + 10*x)*e^(-1)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {10+e (-1+2 x)}{e} \, dx=x^{2} + \frac {x \left (10 - e\right )}{e} \]

[In]

integrate(((-1+2*x)*exp(1)+10)/exp(1),x)

[Out]

x**2 + x*(10 - E)*exp(-1)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {10+e (-1+2 x)}{e} \, dx={\left ({\left (x^{2} - x\right )} e + 10 \, x\right )} e^{\left (-1\right )} \]

[In]

integrate(((-1+2*x)*exp(1)+10)/exp(1),x, algorithm="maxima")

[Out]

((x^2 - x)*e + 10*x)*e^(-1)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.89 \[ \int \frac {10+e (-1+2 x)}{e} \, dx={\left ({\left (x^{2} - x\right )} e + 10 \, x\right )} e^{\left (-1\right )} \]

[In]

integrate(((-1+2*x)*exp(1)+10)/exp(1),x, algorithm="giac")

[Out]

((x^2 - x)*e + 10*x)*e^(-1)

Mupad [B] (verification not implemented)

Time = 0.32 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84 \[ \int \frac {10+e (-1+2 x)}{e} \, dx=\frac {{\mathrm {e}}^{-2}\,{\left (\mathrm {e}\,\left (2\,x-1\right )+10\right )}^2}{4} \]

[In]

int(exp(-1)*(exp(1)*(2*x - 1) + 10),x)

[Out]

(exp(-2)*(exp(1)*(2*x - 1) + 10)^2)/4