IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

nics

find the integral over 1 / 1 + sin x

thedumbheadwithnobrain

x=2tan^-1t

sinx=2t/(1+t²)

dx=2dt/(1+t²)

2 int dt/(t²+2t+1)

2 (-1/sinx+1)+C

rohitkuruvila

int 1/(1+sin x)

multiply and divide by (1 - sin x)

int (1 - sin x)/(1 - sin² x)

int [(1 - sin x)/cos² x]

int [sec²x - sec x tan x]

tan x -sec x +c

karthik2007

$\int \frac{1}{1+sinx} \, dx = \int \frac{1}{1+cos(\frac{\pi}{2} - x)} \, dx = \frac{1}{2} \int sec^2 (\frac{\pi}{4} - \frac{x}{2})\, dx$ which can be easily integrated

ankitagg

write sinx as 2tan x/2/1+tan^2 x/2

now

put tanx/2=t

2sec^2 x/2 dx=dt

now make whole sq. at den. and u will get answer

venkat_tatolu

According to the options we have to proceed.we can choose one of above methods

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