Given `int_(0)^(g(x))f(t)dt=h(x)+C,` where `g(x)` is a polynomial and `C` is arbitrary constant, then On the basis of above information, answer the following questions:
If `g(x)=x, f(t)=((t-|t|)^(2))/(1+t^(2)),` then `h(x)` will be equal to

If f(x)=e^(g(x)) and g(x)=int_(2)^(x)(dt)/(1+t^(4)) then f'(2) is equal to

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :

Let f,g, h be 3 functions such that f(x)gt0 and g(x)gt0, AA x in R where int f(x)*g(x)dx=(x^(4))/(4)+C and int(f(x))/(g(x))dx=int(g(x))/(h(x))dx=ln|x|+C . On the basis of above information answer the following questions: int f(x)*g(x)*h(x)dx is equal to

If f(x)=int_(1)^(x) (log t)/(1+t) dt"then" f(x)+f((1)/(x)) is equal to

If f(x)=cos-int_(0)^(x)(x-t)f(t)dt, then f'(x)+f(x) equals

if f(x) = int_(0)^(x) (t^2+2t+2) dt where x in [2,4] then

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

If F(x)=int_(1)^(x)(ln t)/(1+t+t^(2))dt then F(x)=-F((1)/(x))

If int_(0)^(x)((t^(3)+t)dt)/((1+3t^(2)))=f(x) , then int_(0)^(1)f^(')(x) dx is equal to

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then the value of (23)/(2)f(0) is equal to