let f(x) =∫_0 ^π (dt/(x+sint)) with xreal
1) find a explicit form of f(x)
2) find also g(x) =∫_0 ^π (dt/((x+sint)^2 ))
3) give f^((n)) (x) at form of integral
4) calculate ∫_0 ^π (dt/(3+sint)) and ∫_0 ^π (dt/((3+sint)^2 ))
let f(x) =∫_0 ^1 lnt ln(1−xt)dt with ∣x∣<1
1)determine a explicit form for f(x)
2) find also g(x) =∫_0 ^1 ((tlnt)/(1−xt))dt
3) give f^((n)) (x) at form of integral
4) calculate ∫_0 ^1 ln(t)ln(1−t)dt and ∫_0 ^1 ln(t)ln(2−t)dt
5) calculate ∫_0 ^1 ((tln(t))/(2−t)) dt .