Applications of integration

Differentiate y=5x(e3x) with respect to x and hence find ∫x(e3x) dx Solution: 1/3(x)(e3x) – 1/9(e3x) + C Y = 5x e3x dy/dx = 5x(e3x)(3) + 5 e3x dy/dx = 15x(e3x) + 5(e3x) ∫15x(e3x) + 5(e3x) dx = 5x(e3x) ∫15x(e3x) dx + (5(e3x))/3 = 5x(e3x) 15∫x(e3x) dx = 5x(e3x) – 5/3(e3x) ∫x(e3x) dx = 1/3(x)(e3x) – 1/9(e3x) + […]