3.29 \(\int (10 e)^x \, dx\)

Optimal. Leaf size=12 \[ \frac{(10 e)^x}{1+\log (10)} \]

[Out]

(10*E)^x/(1 + Log[10])

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Rubi [A]  time = 0.0055997, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2194} \[ \frac{(10 e)^x}{1+\log (10)} \]

Antiderivative was successfully verified.

[In]

Int[(10*E)^x,x]

[Out]

(10*E)^x/(1 + Log[10])

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{align*} \int (10 e)^x \, dx &=\frac{(10 e)^x}{1+\log (10)}\\ \end{align*}

Mathematica [A]  time = 0.0036176, size = 12, normalized size = 1. \[ \frac{(10 e)^x}{\log (10 e)} \]

Antiderivative was successfully verified.

[In]

Integrate[(10*E)^x,x]

[Out]

(10*E)^x/Log[10*E]

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Maple [A]  time = 0.01, size = 13, normalized size = 1.1 \begin{align*}{\frac{ \left ( 10\,E \right ) ^{x}}{\ln \left ( 10\,E \right ) }} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*E)^x,x)

[Out]

1/ln(10*E)*(10*E)^x

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Maxima [A]  time = 0.930965, size = 16, normalized size = 1.33 \begin{align*} \frac{\left (10 \, E\right )^{x}}{\log \left (10 \, E\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*E)^x,x, algorithm="maxima")

[Out]

(10*E)^x/log(10*E)

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Fricas [A]  time = 1.96663, size = 27, normalized size = 2.25 \begin{align*} \frac{\left (10 \, E\right )^{x}}{\log \left (10 \, E\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*E)^x,x, algorithm="fricas")

[Out]

(10*E)^x/log(10*E)

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Sympy [A]  time = 0.087169, size = 8, normalized size = 0.67 \begin{align*} \frac{\left (10 e\right )^{x}}{1 + \log{\left (10 \right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*E)**x,x)

[Out]

(10*E)**x/(1 + log(10))

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Giac [A]  time = 1.08015, size = 16, normalized size = 1.33 \begin{align*} \frac{\left (10 \, E\right )^{x}}{\log \left (10 \, E\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((10*E)^x,x, algorithm="giac")

[Out]

(10*E)^x/log(10*E)