Mathematics

Find the following integral.
$$\displaystyle\int e^x (\sec^2 x + \tan x).dx$$


SOLUTION
Now,
$$\displaystyle\int e^x (\sec^2 x + \tan x).dx$$
$$=\displaystyle\int e^x (\sec^2 x ).dx+$$$$\displaystyle\int e^x ( \tan x).dx$$
$$=e^x\displaystyle\int\sec^2 x.dx-\displaystyle\int e^x ( \tan x).dx$$$$+\displaystyle\int e^x ( \tan x).dx$$  [Using method of by parts]
$$=e^x.\tan x-\displaystyle\int e^x ( \tan x).dx$$$$+\displaystyle\int e^x ( \tan x).dx$$
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Subjective Medium Published on 17th 09, 2020
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