`"If " int sqrt("cosec"x+1)dx=k fog(x)+c, " where " k ` is a real constant, then

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))

int " cosec"^(4) 2x dx

int " cosec"^(3) " x dx "

Evaluate : int " cosec"x dx

If int (x+1)/(sqrt(2x-1))dx = f(x)sqrt(2x-1)+C , where C is a constant of integration, then f(x) is equal to

If int(1)/(sqrt(2ax-x^(2)))dx= fog (x)+C , then

int cosec^(2)(x)/(3)dx

Evaluate int "cosec"^(4)x dx

If the solution of the differential equation x^2dy + 2xy dx = sin x dx is x^(k)y + cos x = C (where C is an arbitrary constant), then the value of k is equal to

2. int(sec x + cosec x ) dx