3.49.30 \(\int \frac {1}{30} (6+e^{10}) \, dx\)

Optimal. Leaf size=15 \[ \frac {1}{5} \left (1+x+\frac {e^{10} x}{6}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {8} \begin {gather*} \frac {1}{30} \left (6+e^{10}\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(6 + E^10)/30,x]

[Out]

((6 + E^10)*x)/30

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{30} \left (6+e^{10}\right ) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} \frac {x}{5}+\frac {e^{10} x}{30} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(6 + E^10)/30,x]

[Out]

x/5 + (E^10*x)/30

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fricas [A]  time = 0.90, size = 9, normalized size = 0.60 \begin {gather*} \frac {1}{30} \, x e^{10} + \frac {1}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/30*exp(10)+1/5,x, algorithm="fricas")

[Out]

1/30*x*e^10 + 1/5*x

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giac [A]  time = 0.13, size = 7, normalized size = 0.47 \begin {gather*} \frac {1}{30} \, x {\left (e^{10} + 6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/30*exp(10)+1/5,x, algorithm="giac")

[Out]

1/30*x*(e^10 + 6)

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

method	result	size
default	\(\left (\frac {{\mathrm e}^{10}}{30}+\frac {1}{5}\right ) x\)	\(9\)
norman	\(\left (\frac {{\mathrm e}^{10}}{30}+\frac {1}{5}\right ) x\)	\(9\)
risch	\(\frac {x \,{\mathrm e}^{10}}{30}+\frac {x}{5}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/30*exp(10)+1/5,x,method=_RETURNVERBOSE)

[Out]

(1/30*exp(10)+1/5)*x

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maxima [A]  time = 0.35, size = 7, normalized size = 0.47 \begin {gather*} \frac {1}{30} \, x {\left (e^{10} + 6\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/30*exp(10)+1/5,x, algorithm="maxima")

[Out]

1/30*x*(e^10 + 6)

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mupad [B]  time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} x\,\left (\frac {{\mathrm {e}}^{10}}{30}+\frac {1}{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(10)/30 + 1/5,x)

[Out]

x*(exp(10)/30 + 1/5)

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sympy [A]  time = 0.04, size = 8, normalized size = 0.53 \begin {gather*} x \left (\frac {1}{5} + \frac {e^{10}}{30}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/30*exp(10)+1/5,x)

[Out]

x*(1/5 + exp(10)/30)

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