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Evaluate
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Differentiate w.r.t. x
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\frac{\int 2^{x}\mathrm{d}x}{9e^{4}+4}
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
\frac{2^{x}}{\ln(2)\left(9e^{4}+4\right)}
Use \int p^{q}\mathrm{d}q=\frac{p^{q}}{\ln(p)} from the table of common integrals to obtain the result.
\frac{2^{x}}{\left(9e^{4}+4\right)\ln(2)}
Simplify.
\frac{2^{x}}{\left(9e^{4}+4\right)\ln(2)}+С
If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.