Evaluate
\frac{728}{729\ln(3)}\approx 0.908990613
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\int \left(\frac{1}{3}\right)^{x}\mathrm{d}x
Evaluate the indefinite integral first.
\frac{\left(\frac{1}{3}\right)^{x}}{\ln(\frac{1}{3})}
Use \int x^{y}\mathrm{d}y=\frac{x^{y}}{\ln(x)} from the table of common integrals to obtain the result.
-\frac{\left(\frac{1}{3}\right)^{x}}{\ln(3)}
Simplify.
-\left(\frac{1}{3}\right)^{6}\ln(3)^{-1}+\left(\frac{1}{3}\right)^{0}\ln(3)^{-1}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\frac{728}{729\ln(3)}
Simplify.
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