Integration By Parts

Integration By Parts

1. Performing Integration By Parts $\int f(x)g'(x)\,dx=f(x)g(x)-\int f'(x)g(x)\,dx$

1. Performing Integration By Parts $\int u\,dv=uv-\int v\,du$

Explaining

When you are looking at this equation

$\int u\,dv=uv-\int v\,du$

you may have been confused by u,du,v,dv

you can just under stand it as

1. u = f(x)
2. du = f'(x)
3. v = g(x)
4. dv = g'(x)

so by looking at u and v as a function we you say du or dv is derivative of that function.

for example if we say u is f(x) than du is derivative of f(x) so it will be f'(x).

$\int u\,dv=uv-\int v\,du$

can be think as

$\int f(x)\,g'(x)=(f(x)*g(x))-\int g(x)\,f'(x)$