Mathematics

Evaluate the following integral:
$$\int { { 3 }^{ x } } dx$$


SOLUTION
Given $$\displaystyle \int{{3}^{x}dx}$$

Let $$t={3}^{x}$$ 

$$\Rightarrow\,\log{t}=x\log{3}$$

$$\Rightarrow\,\dfrac{dt}{t}=\log{3}dx$$

$$\Rightarrow\,\dfrac{1}{\log{3}}dt=tdx$$

$$\Rightarrow\,\dfrac{1}{\log{3}}dt={3}^{x}dx$$

$$\displaystyle \int{{3}^{x}dx}$$
$$=\displaystyle \int{\dfrac{1}{\log{3}}dt}$$

$$=\dfrac{1}{\log{3}}t+c$$ where $$c$$ is the constant of integration
$$=\dfrac{1}{\log{3}}{3}^{x}+c$$ 

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Subjective Medium Published on 17th 09, 2020
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