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

Optimal. Leaf size=15 \[ \frac {4}{5} \left (5+\left (21+e^{3/16}\right ) x\right ) \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 12, normalized size of antiderivative = 0.80, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8} \begin {gather*} \frac {4}{5} \left (21+e^{3/16}\right ) x \end {gather*}

Antiderivative was successfully verified.

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

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 16, normalized size = 1.07 \begin {gather*} \frac {84 x}{5}+\frac {4}{5} e^{3/16} x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(84 + 4*E^(3/16))/5,x]

[Out]

(84*x)/5 + (4*E^(3/16)*x)/5

________________________________________________________________________________________

fricas [A]  time = 0.74, size = 9, normalized size = 0.60 \begin {gather*} \frac {4}{5} \, x e^{\frac {3}{16}} + \frac {84}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4/5*x*e^(3/16) + 84/5*x

________________________________________________________________________________________

giac [A]  time = 0.24, size = 7, normalized size = 0.47 \begin {gather*} \frac {4}{5} \, x {\left (e^{\frac {3}{16}} + 21\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4/5*x*(e^(3/16) + 21)

________________________________________________________________________________________

maple [A]  time = 0.01, size = 9, normalized size = 0.60

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

maxima [A]  time = 0.36, size = 7, normalized size = 0.47 \begin {gather*} \frac {4}{5} \, x {\left (e^{\frac {3}{16}} + 21\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

4/5*x*(e^(3/16) + 21)

________________________________________________________________________________________

mupad [B]  time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} x\,\left (\frac {4\,{\mathrm {e}}^{3/16}}{5}+\frac {84}{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*exp(3/16))/5 + 84/5,x)

[Out]

x*((4*exp(3/16))/5 + 84/5)

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 12, normalized size = 0.80 \begin {gather*} x \left (\frac {4 e^{\frac {3}{16}}}{5} + \frac {84}{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x*(4*exp(3/16)/5 + 84/5)

________________________________________________________________________________________