∫e^x(2+sin⁡2x)/(1+cos⁡2x) dx=

Correct answer: (A) e^xtan⁡x+C. I= ∫ e^x ( (2+2sinxcosx)/(2cos^2 x) )dx I= ∫ e^x ( tanx+sec^2 x )dx I=e^x tanx+C ∵ ∫ e^x f x + f^(′) x dx = e^x · f + C

Q85 / 150 · MHT CET 2018 · Mathematics

$\int e^{x} [\frac{2 + \sin 2 x}{1 + \cos 2 x}] d x =$

Correct answer
A
$e^{x} \tan x + C$
B
$e^{x} + \tan x + C$
C
$2 e^{x} \tan x + C$
D
$e^{x} \tan 2 x + C$

Solution

I = \int e^{x} (\frac{2 + 2 \sin x \cos x}{2 \cos^{2} x}) d x

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

I = e^{x} \tan x + C

[∵ \int e^{x} (f (x) + f^{'} (x)) dx = e^{x} \cdot f + C]

Hence, the correct answer is option: 'A'.

∫ex2+sin⁡2x1+cos⁡2x dx=

Solution

Relevant Questions

$\int e^{x} [\frac{2 + \sin 2 x}{1 + \cos 2 x}] d x =$