Integration by Parts

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Integration by PartsIntegration by Parts is a special method of integration that is often useful when two functions are multiplied together but is also helpful in other ways. ∫u v dx = u∫v dx −∫u' (∫v dx) dx
  • u is the function u(x)
  • v is the function v(x)
  • u' is the derivative of the function u(x)
So we followed these steps:
  • Choose u and v
  • Differentiate u: u'
  • Integrate v: ∫v dx
  • Put u, u' and ∫v dx into: u∫v dx −∫u' (∫v dx) dx
  • Simplify and solve
In English we can say that ∫u v dx becomes:(u integral v) minus integral of (derivative u, integral v)