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we know formula of integration by part is ∫uv' dx = uv − ∫u'v dx plz explain stepwise process to make left hand side more easier how to convert ∫uv' dx = uv − ∫u'v dx into ∫uv dx = u∫v dx − ∫u'(∫v dx) dx

we know formula of integration by part is  ∫uv' dx = uv − ∫u'v dx
plz explain stepwise process to make left hand side more easier
how to convert ∫uv' dx = uv − ∫u'v dx      
into ∫uv dx = u∫v dx − ∫u'(∫v dx) dx

Grade:12th pass

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
5 years ago
dear student,

we know this formula
∫uv' dx = uv − ∫u'v dx

now put v’= w

So , ∫uw dx = uv − ∫u’ (∫w dx) dx

Now replace w=v

So,
∫uv dx = u∫v dx − ∫u'(∫v dx) dx

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