3.44.65 \(\int (1+20 e^5+e^x) \, dx\)

Optimal. Leaf size=14 \[ e^x+x+20 \left (6+e^5 x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2194} \begin {gather*} \left (1+20 e^5\right ) x+e^x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 + 20*E^5 + E^x,x]

[Out]

E^x + (1 + 20*E^5)*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} &=\left (1+20 e^5\right ) x+\int e^x \, dx\\ &=e^x+\left (1+20 e^5\right ) x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.79 \begin {gather*} e^x+x+20 e^5 x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 + 20*E^5 + E^x,x]

[Out]

E^x + x + 20*E^5*x

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fricas [A]  time = 0.49, size = 9, normalized size = 0.64 \begin {gather*} 20 \, x e^{5} + x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+20*exp(5)+1,x, algorithm="fricas")

[Out]

20*x*e^5 + x + e^x

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giac [A]  time = 0.17, size = 9, normalized size = 0.64 \begin {gather*} 20 \, x e^{5} + x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+20*exp(5)+1,x, algorithm="giac")

[Out]

20*x*e^5 + x + e^x

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maple [A]  time = 0.02, size = 10, normalized size = 0.71

method	result	size
default	\(x +20 x \,{\mathrm e}^{5}+{\mathrm e}^{x}\)	\(10\)
risch	\(x +20 x \,{\mathrm e}^{5}+{\mathrm e}^{x}\)	\(10\)
norman	\(\left (20 \,{\mathrm e}^{5}+1\right ) x +{\mathrm e}^{x}\)	\(12\)
derivativedivides	\({\mathrm e}^{x}+\left (20 \,{\mathrm e}^{5}+1\right ) \ln \left ({\mathrm e}^{x}\right )\)	\(14\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x)+20*exp(5)+1,x,method=_RETURNVERBOSE)

[Out]

x+20*x*exp(5)+exp(x)

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maxima [A]  time = 0.35, size = 9, normalized size = 0.64 \begin {gather*} 20 \, x e^{5} + x + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+20*exp(5)+1,x, algorithm="maxima")

[Out]

20*x*e^5 + x + e^x

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mupad [B]  time = 3.06, size = 11, normalized size = 0.79 \begin {gather*} {\mathrm {e}}^x+x\,\left (20\,{\mathrm {e}}^5+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20*exp(5) + exp(x) + 1,x)

[Out]

exp(x) + x*(20*exp(5) + 1)

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sympy [A]  time = 0.07, size = 10, normalized size = 0.71 \begin {gather*} x \left (1 + 20 e^{5}\right ) + e^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(x)+20*exp(5)+1,x)

[Out]

x*(1 + 20*exp(5)) + exp(x)

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