Question

求f(x)=积分[1,x] sin(sqrt(t)/(5t^2+cos(3*t))的导数,

Answer 1

f(x)= ∫ (1->x) sin(√t/[5t^2+cos3t]) dt

let

dF(t) = sin(√t/[5t^2+cos3t]) dt

f(x) = ∫ (1->x) sin(√t/[5t^2+cos3t]) dt

= ∫ (1->x) dF(t)

= F(x) - F(1)

f'(x) = F'(x)

= sin(√x/[5x^2+cos3x])