Page:Calculus Made Easy.pdf/247

 Examples.

(1) Find $$\int w \cdot \sin w\, dw$$.

Write $$u=w$$, and for $$\sin w \cdot dw$$ write $$dx$$. We shall then have du=dw, while $$\int \sin w \cdot dw = -\cos w = x$$.

Putting these into the formula, we get

(2) Find $$\int x \epsilon^x\, dx$$.

and

(3) Try $$\int \cos^2 \theta\, d\theta$$.