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

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

[Out]

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

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Rubi [A]  time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, 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*}

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Mathematica [A]  time = 0.00, size = 12, normalized size = 1.00 \[ \frac {(10 e)^x}{\log (10 e)} \]

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [A]  time = 0.41, size = 12, normalized size = 1.00 \[ \frac {\left (10 \, E\right )^{x}}{\log \left (10 \, E\right )} \]

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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giac [A]  time = 0.96, size = 12, normalized size = 1.00 \[ \frac {\left (10 \, E\right )^{x}}{\log \left (10 \, E\right )} \]

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)

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maple [A]  time = 0.02, size = 13, normalized size = 1.08 \[ \frac {\left (10 E \right )^{x}}{\ln \left (10 E \right )} \]

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 = 0.47, size = 12, normalized size = 1.00 \[ \frac {\left (10 \, E\right )^{x}}{\log \left (10 \, E\right )} \]

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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mupad [B]  time = 0.07, size = 12, normalized size = 1.00 \[ \frac {{10}^x\,{\mathrm {e}}^x}{\ln \left (10\right )+1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*exp(1))^x,x)

[Out]

(10^x*exp(x))/(log(10) + 1)

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sympy [A]  time = 0.09, size = 10, normalized size = 0.83 \[ \frac {\left (10 e\right )^{x}}{1 + \log {\left (10 \right )}} \]

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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