What is the simples way to integrate by part?

In a case of integral that you want to integrate once using technique "by parts" you have to divide your integral into two functions.Working on an example, f(x)=x sinxLet g(x)=x and h'(x)= sin x Then we integrate the derivative of a smaller function and we find the derivative of a normal funtion.x'=1 and h(x)= -cos(x)The result of this function is -cos(x)x - integral of 1*(-cos (x)).
Then we have-cos(x)x +integral of cos(x)
-cos(x)x +sin(x)
And this is our final answer