Let `g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0.` then the value of `8g(pi/2)` is __________

If f(x)=int(3x^2+1)/((x^2-1)^3)dxa n df(0)=0, then the value of |2/(f(2))| is___

Let z=(cosx)^5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=(2pi)/9 is____________.

lim_(xto0)(1-cosx)/x^(2)

IfI=int_0^((3pi)/5)(1+x)sinx+(1-x)cosx)dx , then value of (sqrt(2)-1)I is_____

int_(0)^(pi)(cosx)/(1+sinx)dx=

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

Let f(x)=int_0^x(dt)/(sqrt(1+t^3))a n dg(x) be the inverse of f(x) . Then the value of 4(g^(primeprime)(x))/((g(x))^2)i s____

Let g(x) be differentiable on R and int_(sint)^1x^2g(x)dx=(1-sint), where t in (0,pi/2)dot Then the value of g(1/(sqrt(2))) is____

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)