3.29 \(\int 10^{2+5 x} \, dx\)

Optimal. Leaf size=19 \[ \frac{2^{5 x+2} 5^{5 x+1}}{\log (10)} \]

[Out]

(2^(2 + 5*x)*5^(1 + 5*x))/Log[10]

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Rubi [A]  time = 0.0054357, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {2194} \[ \frac{2^{5 x+2} 5^{5 x+1}}{\log (10)} \]

Antiderivative was successfully verified.

[In]

Int[10^(2 + 5*x),x]

[Out]

(2^(2 + 5*x)*5^(1 + 5*x))/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^{2+5 x} \, dx &=\frac{2^{2+5 x} 5^{1+5 x}}{\log (10)}\\ \end{align*}

Mathematica [A]  time = 0.0049009, size = 19, normalized size = 1. \[ \frac{2^{5 x+2} 5^{5 x+1}}{\log (10)} \]

Antiderivative was successfully verified.

[In]

Integrate[10^(2 + 5*x),x]

[Out]

(2^(2 + 5*x)*5^(1 + 5*x))/Log[10]

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Maple [A]  time = 0.013, size = 14, normalized size = 0.7 \begin{align*}{\frac{{10}^{2+5\,x}}{5\,\ln \left ( 10 \right ) }} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10^(2+5*x),x)

[Out]

1/5/ln(10)*10^(2+5*x)

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Maxima [A]  time = 1.13901, size = 18, normalized size = 0.95 \begin{align*} \frac{10^{5 \, x + 2}}{5 \, \log \left (10\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10^(2+5*x),x, algorithm="maxima")

[Out]

1/5*10^(5*x + 2)/log(10)

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Fricas [A]  time = 1.49225, size = 35, normalized size = 1.84 \begin{align*} \frac{10^{5 \, x + 2}}{5 \, \log \left (10\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10^(2+5*x),x, algorithm="fricas")

[Out]

1/5*10^(5*x + 2)/log(10)

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Sympy [A]  time = 0.089954, size = 10, normalized size = 0.53 \begin{align*} \frac{10^{5 x + 2}}{5 \log{\left (10 \right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10**(2+5*x),x)

[Out]

10**(5*x + 2)/(5*log(10))

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Giac [A]  time = 1.23942, size = 18, normalized size = 0.95 \begin{align*} \frac{10^{5 \, x + 2}}{5 \, \log \left (10\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10^(2+5*x),x, algorithm="giac")

[Out]

1/5*10^(5*x + 2)/log(10)