let f(x)=∫_0 ^1 (dt/(t+x+(√(t^2 +1)))) (x real parametre)
1) find a explicite form forf(x)
2)detemine also g(x) =∫_0 ^1 (dt/((t+x+(√(t^2 +1)))^2 ))
3)give f^((n)) (x) at form of integrals
4) find the values of ∫_0 ^1 (dt/(t+(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+(√(t^2 +1)))^2 ))
5) find the values of ∫_0 ^1 (dt/(t+1 +(√(t^2 +1)))) and ∫_0 ^1 (dt/((t+1+(√(t^2 +1)))^2 ))