Question

integration of sin x^2

Answer 1

Let u = x2, then du/dx = 2x or du = 2x dx. Since we have exactly 2x dx in the original integral, we can replace it by du: ∫ 2x cos(x2) dx = ∫ cos u du = sin u + C = sin(x2) + C. This is not the only way to do the algebra, and typically there are many paths to the correct answer.