=∫ 1/2(sin(2x+3x)+sin(2x-3x))dx

= 1/2∫sin 5 xdx- 1/2∫sin xdx

= 1/ 10∫sin5xd 5 x+ 1/2∫dcosx

=(cosx)/2-(cos5x)/ 10+C

Find a solution

Let f(x) be the original function of function F(x). We call all the primitive functions f(x)+c of the function f(x) (where c is an arbitrary constant) indefinite integrals of the function f(x), also called the inverse derivative of the function f (x), and write it as ∫f(x)dx or ∫.

Where ∫ is called an integral symbol, f(x) is called an integrand, x is called an integrand, f(x)dx is called an integrand, and c is called an integral constant or an integral constant. The process of finding the indefinite integral of a known function is called indefinite integral of this function.