Mathematics

Solve $$\int {{e^x}\,\cos e{c^2}\,\left( {{e^x}} \right)\,dx} $$


SOLUTION
$$I=\displaystyle\int e^{x}\csc^{2}(e^{x})dx$$

Let $$e^{x}=t\Rightarrow e^{x}dx=dt$$

$$I=\displaystyle\int\csc^{2}t dt =-\cot (t)+C$$

$$=-\cot (e^{x})+C$$

$$\therefore \displaystyle\int e^{x}\csc^{2} (e^{x})dx=-\cot (e^{x})+C$$
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Subjective Medium Published on 17th 09, 2020
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