Page:Calculus Made Easy.pdf/215

 That is to say, $$x^{2}dx$$ will be changed to $$\tfrac{1}{3} x^3$$. Put this into the equation; but don't forget to add the “constant of integration” $$C$$ at the end. So we get:

You have actually performed the integration. How easy!

Let us try another simple case.

where $$a$$ is any constant multiplier. Well, we found when differentiating (see p. 29) that any constant factor in the value of $$y$$ reappeared unchanged in the value of $$\dfrac{dy}{dx}$$. In the reversed process of integrating, it will therefore also reappear in the value of $$y$$. So we may go to work as before, thus:

So that is done. How easy!