integration by parts

The formula for integration by parts can be derived from the product rule of differentiation:

    \[\;\text{d}(uv)=u\;\text{d}v+v\;\text{d}u\]

Take the indefinite integral of both sides (neglecting the constant of integration)

    \[uv=\int u \;\text{d}v+\int v \;\text{d}u\]

or in the standard form:

    \[\boxed{\int U \;\text{d}V=UV-\int V \;\text{d}U}\]

int by parts


integrationbyparts

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