3.59.86 \(\int (3+4 e^{8+x}) \, dx\)

Optimal. Leaf size=14 \[ 4 e^8 \left (-8+e^x\right )+3 x \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.79, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194} \begin {gather*} 3 x+4 e^{x+8} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3 + 4*E^(8 + x),x]

[Out]

4*E^(8 + x) + 3*x

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=3 x+4 \int e^{8+x} \, dx\\ &=4 e^{8+x}+3 x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} 4 e^{8+x}+3 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3 + 4*E^(8 + x),x]

[Out]

4*E^(8 + x) + 3*x

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fricas [A]  time = 0.73, size = 10, normalized size = 0.71 \begin {gather*} 3 \, x + 4 \, e^{\left (x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(8)*exp(x)+3,x, algorithm="fricas")

[Out]

3*x + 4*e^(x + 8)

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giac [A]  time = 0.14, size = 10, normalized size = 0.71 \begin {gather*} 3 \, x + 4 \, e^{\left (x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(8)*exp(x)+3,x, algorithm="giac")

[Out]

3*x + 4*e^(x + 8)

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maple [A]  time = 0.04, size = 11, normalized size = 0.79

method	result	size
default	\(3 x +4 \,{\mathrm e}^{8} {\mathrm e}^{x}\)	\(11\)
norman	\(3 x +4 \,{\mathrm e}^{8} {\mathrm e}^{x}\)	\(11\)
risch	\(3 x +4 \,{\mathrm e}^{x +8}\)	\(11\)
derivativedivides	\(4 \,{\mathrm e}^{8} {\mathrm e}^{x}+3 \ln \left ({\mathrm e}^{x}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*exp(8)*exp(x)+3,x,method=_RETURNVERBOSE)

[Out]

3*x+4*exp(8)*exp(x)

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maxima [A]  time = 0.36, size = 10, normalized size = 0.71 \begin {gather*} 3 \, x + 4 \, e^{\left (x + 8\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(8)*exp(x)+3,x, algorithm="maxima")

[Out]

3*x + 4*e^(x + 8)

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mupad [B]  time = 4.04, size = 10, normalized size = 0.71 \begin {gather*} 3\,x+4\,{\mathrm {e}}^8\,{\mathrm {e}}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*exp(8)*exp(x) + 3,x)

[Out]

3*x + 4*exp(8)*exp(x)

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sympy [A]  time = 0.07, size = 10, normalized size = 0.71 \begin {gather*} 3 x + 4 e^{8} e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(4*exp(8)*exp(x)+3,x)

[Out]

3*x + 4*exp(8)*exp(x)

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