How can I calculate this integral? How do I get rid of $e^{\tan x}$?
$$\int \frac{\sin x \cdot e^{\tan x}}{\cos^3 x} \,\mathrm dx$$
2026-04-18 02:53:42.1776480822
How can I integrate $\frac{\sin x \cdot e^{\tan x}}{\cos^3 x}$?
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In a more clear form your integrand is $$ \frac{\sin x}{\cos x}\mathrm{e}^{\tan x}\sec^2 x dx $$ Then making the sub $t =\tan x\to dt = \sec^2 x dx$ we find $$ t \mathrm{e}^t dt $$ Which is easier.