Question

求不定积分∫sinx^2(x dx)

∫e^x^3(x^2 dx) ∫sinx^2(x dx)
∫e^cosx(sinx dx) ∫cos √x（1/√x dx）

Answer 1

∫[sin(x)]^2dx=(1/2)∫(1-cos2x)dx=x/2-(1/4)sin2x +c
sin(x) = x - x^3/3! + x^5/5!-.
sin(x^2) = x^2 - x^6/3! + x^10/5! -..
Fresnel integrals
∫(0,x)sin(x^2)dx=∑(0,∞) (-1)^n x^(4n+3)/[(2n+1)!(4n+3)]