∫ e^x(tan x+ ^2 x)dx ∫ e^x(f( x+f^'(x))dx= e^x f(x) Here f(x)=tan x f^'(x)= ^2 x e^x tan x ...

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Special Integrals - 1

∫ extan x+ 2 ...

Question

$\int e^{x} (tan x + {sec}^{2} x) d x$

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Solution

$\int e^{x} (tan x + {sec}^{2} x) d x$
$\int e^{x} (f (x + f^{'} (x)) d x = e^{x} f (x)$
Here $f (x) = tan x ⟹ f^{'} (x) = {sec}^{2} x$
$⟹ e^{x} tan x$

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