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)/ln(10)

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Rubi [A]  time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, 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*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 1.00 \[ \frac {2^{5 x+2} 5^{5 x+1}}{\log (10)} \]

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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fricas [A]  time = 0.40, size = 13, normalized size = 0.68 \[ \frac {10^{5 \, x + 2}}{5 \, \log \left (10\right )} \]

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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giac [A]  time = 0.36, size = 13, normalized size = 0.68 \[ \frac {10^{5 \, x + 2}}{5 \, \log \left (10\right )} \]

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)

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maple [A]  time = 0.01, size = 14, normalized size = 0.74 \[ \frac {10^{5 x +2}}{5 \ln \left (10\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.43, size = 13, normalized size = 0.68 \[ \frac {10^{5 \, x + 2}}{5 \, \log \left (10\right )} \]

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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mupad [B]  time = 0.09, size = 11, normalized size = 0.58 \[ \frac {20\,{10}^{5\,x}}{\ln \left (10\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10^(5*x + 2),x)

[Out]

(20*10^(5*x))/log(10)

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sympy [A]  time = 0.09, size = 10, normalized size = 0.53 \[ \frac {10^{5 x + 2}}{5 \log {\left (10 \right )}} \]

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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