`intsqrt((c o s e c x-cotx)/(c o s e c x+cotx))*(secx)/(sqrt(1+2secx))dx`

Evaluate: intsqrt(("cosec"x-cotx)/("cosec"x+cotx).(secx)/sqrt(1+2secx) dx

int(secx)/(1+c o s e c x)dx

int(sec^2x)/(c o s e c^2x)dx

int((secx+ "cosec x")(secx- "cosec x"))/(tanx +cotx)dx=

If intsqrt(cos e cx+1)dx=kfog(x)+c ,w h e r ek is a real constant, then (a) k=-2,f(x)=cot^(-1)x ,g(x)=sqrt(cos e cx-1) (b) k=-2,f(x)=tan^(-1)x ,g(x)=sqrt(cos e cx-1) (c) k=2,f(x)=tan^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1)) (d) k=2,f(x)=cot^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1))

If intsqrt(cos e cx+1)dx=kfog(x)+c ,w h e r ek is a real constant, then (a). k=-2,f(x)=cot^(-1)x ,g(x)=sqrt(cos e cx-1) (b) k=-2,f(x)=tan^(-1)x ,g(x)=sqrt(cos e cx-1) (c) k=2,f(x)=tan^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1)) (d) k=2,f(x)=cot^(-1)xg(x)=(cotx)/(sqrt(cos e cx-1))

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)