If `int_0^1(e^t)/(1+t)dt=a ,` then find the value of `int_0^1(e^t)/((1+t)^2)dt` in terms of `a` .

If int_0^1e^-(x^2)dx=a , then find the value of int_0^1x^2e^-(x^2)dx in terms of a .

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

If int_0^1 (e^t dt)/(t+1)=a, then evaluate int_(b-1)^b (e^t dt)/(t-b-1)

If f(x)=1+1/x int_1^x f(t) dt, then the value of (e^-1) is

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

f(x)=int_1^x(tan^(-1)(t))/t dt , x in R^+, then find the value of f(e^2)-f(1/(e^2))

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..