Question

If \(u\) and \(v\) are differentiable functions, which formula is used for integration by parts?

Options

• \[\int u\,dv=uv-\int v\,du\]

• \[\int u\,dv=uv+\int v\,du\]

• \[\int u\,dv=\int v\,du-uv\]

• \[\int u\,dv=vu-\int u\,dv\]

Answer 1

The integration-by-parts formula is \(\int u\,dv=uv-\int v\,du\). Here, \(v\) is obtained by integrating \(dv\), while \(du\) is obtained by differentiating \(u\).