If `intsqrt(1+sinx)f(x)dx=2/3(1+sinx)^(3/2)+c ,t h e nf(x)e q u a l` `cosx` (b) `sinx` (c) `tanx` (d) 1

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

("lim")_(xto0)((1+tanx)/(1+sinx))^(cos e cx)i se q u a l t o (a)e (b) 1/e (c) 1 (d) none of these

If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h e nai se q u a l 1/3 (b) 2/3 (c) -1/3 (d0 -2/3

Evaluate int(cosx)/((1-sinx)(2+sinx))dx

Find f'(x) , given f(x)=(cosx)/(1+sinx)

If y=(sinx)^(tanx),t h e n(dy)/(dx)= (a) (sinx)^(tanx)(1+sec^2xlogsinx) (b) tanx(sinx)^(tanx-1)cosx (c) (sinx)^(tanx) (d) sec^2xlogsinx tanx(sinx)^(tanx-1)

If int f(x) sinx cosx dx=(1)/(2(b^(2)-a^(2))) "In " f(x)+c," then " f(x) is equal to

If f(x)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

If f(x)=(log)_x(lnx),t h e nf^(prime)(x) at x=e is equal to 1/e (b) e (c) 1 (d) zero

Prove that: (1−sinx)/(1+sinx) =(secx−tanx)^2