Mathematics

Evaluate the following integral
$$\displaystyle\int{\dfrac{{e}^{3x}}{{e}^{3x}+1}dx}$$


SOLUTION
$$\displaystyle\int{\dfrac{{e}^{3x}}{{e}^{3x}+1}dx}$$

$$t={e}^{3x}+1\Rightarrow\,dt=3{e}^{3x}\,dx$$

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

$$=\dfrac{1}{3}\displaystyle\int{\dfrac{dt}{t}}$$

$$=\dfrac{1}{3}\log{\left|{e}^{3x}+1\right|}+c$$
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Subjective Medium Published on 17th 09, 2020
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