Question

integrate the function sinx/(1 + cosx).dx

Answer 1

this is answer.........

Answer 2

HELLO DEAR,

$\bold{\int{\frac{sinx}{1 + cosx}}\,dx}$

now, let cosx = t $\bold{\Rightarrow -sinx = dt/dx}$

$\bold{\Rightarrow dx = -dt/sinx}$

now substitute the value of dx in the function

$\bold{\int{\frac{sinx}{1 + t}*\frac{dt}{-sinx}}}$

$\bold{-\int{\frac{1}{1 + t}}\,dt}$

$\bold{-\log|1 + t| + C}$

$\bold{-\log|1 + cosx|}$

where, c is the arbitrary constant.

hence, the integral of sinx/(1 + cosx) is (-log|1 + cosx|)


I HOPE ITS HELP YOU DEAR,
THANKS