`int (1-cosx)"cosec"^(2)x dx=f(x)+c rArr f(x)=`

int(1-cosx)cosec^(2)x dx is equal to

int (sinx)/(cos x(1+ cos x))dx= f(x)+ c rArr f(x)=

int (dx)/(x^(2)+2x+2)= f(x)+c rArr f(x)=

int (dx)/(x^(2)-2x+2)= f(x)+c rArr f(x)=

int (sqrt(cotx))/(sin xcos x)dx=-f (x)+c rArr f(x)=

int (3-x^(2))/(1-2x+x^(2))e^(x)dx=e^(x)f(x)+c rArr f(x)=

I : int (dx)/(sqrt(x)(x+9))=f(x)+c constnat, then f(x)=(2)/(3)Tan^(-1)((sqrt(x))/(3)) II : int (dx)/((x+100)sqrt(x+99))=f(x) +c rArr f(x)=2 Tan^(-1)sqrt(x+99)

int (dx)/((x+100)sqrt(x+99))=f(x)+c rArr f(x)=

int(dx)/("cosec"x+cosx)=

int Sin^(-1)((2x)/(1+x^(2)))dx=f(x)-log (1+x^(2))+c rArr f(x)=