e^x (1 + x + ^2 x) , ,dx = - Vidyadip

MCQ

$\int {{e^x}(1 + \tan x + {{\tan }^2}x)\,\,dx = } $

A
${e^x}\sin x + c$
B
${e^x}\cos x + c$
✓
${e^x}\tan x + c$
D
${e^x}\sec x + c$

✓

Answer

Correct option: C.

${e^x}\tan x + c$

c
(c) $I = \int {{e^x}(1 + \tan x + {{\tan }^2}x} )dx$
==>$\int {{e^x}(1 + \tan x + {{\tan }^2}x)dx = \int {{e^x}(\tan x + {{\sec }^2}x)} \,dx.} $$I = {e^x}\tan x + c$

$(\,\int {{e^x}[f(x) + f'(x)] + x = {e^x}f(x) + c} ).$

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