\(\int \frac {1}{5} (84+4 e^{3/16}) \, dx\) [7964]

Optimal result

Integrand size = 13, antiderivative size = 15 \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=\frac {4}{5} \left (5+\left (21+e^{3/16}\right ) x\right ) \]

[Out]

4+4/5*x*(exp(3/16)+21)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8} \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=\frac {4}{5} \left (21+e^{3/16}\right ) x \]

[In]

Int[(84 + 4*E^(3/16))/5,x]

[Out]

(4*(21 + E^(3/16))*x)/5

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps \begin{align*} \text {integral}& = \frac {4}{5} \left (21+e^{3/16}\right ) x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07 \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=\frac {84 x}{5}+\frac {4}{5} e^{3/16} x \]

[In]

Integrate[(84 + 4*E^(3/16))/5,x]

[Out]

(84*x)/5 + (4*E^(3/16)*x)/5

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53

method	result	size
default	\(\frac {4 x \left ({\mathrm e}^{\frac {3}{16}}+21\right )}{5}\)	\(8\)
norman	\(\left (\frac {4 \,{\mathrm e}^{\frac {3}{16}}}{5}+\frac {84}{5}\right ) x\)	\(9\)
parallelrisch	\(\left (\frac {4 \,{\mathrm e}^{\frac {3}{16}}}{5}+\frac {84}{5}\right ) x\)	\(9\)
risch	\(\frac {4 \,{\mathrm e}^{\frac {3}{16}} x}{5}+\frac {84 x}{5}\)	\(10\)
parts	\(\frac {4 \,{\mathrm e}^{\frac {3}{16}} x}{5}+\frac {84 x}{5}\)	\(10\)

[In]

int(4/5*exp(3/16)+84/5,x,method=_RETURNVERBOSE)

[Out]

4/5*x*(exp(3/16)+21)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=\frac {4}{5} \, x e^{\frac {3}{16}} + \frac {84}{5} \, x \]

[In]

integrate(4/5*exp(3/16)+84/5,x, algorithm="fricas")

[Out]

4/5*x*e^(3/16) + 84/5*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=x \left (\frac {4 e^{\frac {3}{16}}}{5} + \frac {84}{5}\right ) \]

[In]

integrate(4/5*exp(3/16)+84/5,x)

[Out]

x*(4*exp(3/16)/5 + 84/5)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=\frac {4}{5} \, x {\left (e^{\frac {3}{16}} + 21\right )} \]

[In]

integrate(4/5*exp(3/16)+84/5,x, algorithm="maxima")

[Out]

4/5*x*(e^(3/16) + 21)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=\frac {4}{5} \, x {\left (e^{\frac {3}{16}} + 21\right )} \]

[In]

integrate(4/5*exp(3/16)+84/5,x, algorithm="giac")

[Out]

4/5*x*(e^(3/16) + 21)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \frac {1}{5} \left (84+4 e^{3/16}\right ) \, dx=x\,\left (\frac {4\,{\mathrm {e}}^{3/16}}{5}+\frac {84}{5}\right ) \]

[In]

int((4*exp(3/16))/5 + 84/5,x)

[Out]

x*((4*exp(3/16))/5 + 84/5)