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Grade 12th passIntegral Calculus

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

Profile image of dipak shah
10 Years agoGrade 12th pass
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1 Answer

Profile image of Nishant Vora
10 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