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

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

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

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

Evaluate int_(-oo)^(0)(te^(t))/(sqrt(1-e^(2t)))dt

If int_0^x(f(t))dt=x+int_x^1(t^2.f(t))dt+pi/4-1 , then the value of the integral int_-1^1(f(x))dx is equal to

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.

If f(x)=int_(0)^(x)|t-1|dt , where 0lexle2 , then

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