Find the integral int(18^x+e^(18x))dx

 Exercise

$\int18^x+e^{18x}dx$

 

Expand the integral $\int\left(18^x+e^{18x}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int18^xdx+\int e^{18x}dx$

 

The integral $\int18^xdx$ results in: $\frac{18^x}{\ln\left(18\right)}$

$\frac{18^x}{\ln\left(18\right)}$

 

The integral $\int e^{18x}dx$ results in: $\frac{1}{18}e^{18x}$

$\frac{1}{18}e^{18x}$

 

Gather the results of all integrals

$\frac{18^x}{\ln\left|18\right|}+\frac{1}{18}e^{18x}$

 

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{18^x}{\ln\left|18\right|}+\frac{1}{18}e^{18x}+C_0$

$\frac{18^x}{\ln\left|18\right|}+\frac{1}{18}e^{18x}+C_0$

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