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Chapter – Indefinite Integral

Sub Topic – Integrals of some more Types

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Outline

  • Integrals of some more Types

  • Examples

  • Assignments

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Integral of the type :

= f(x)

[Take u = f(x), dv =

Proof :

]

+C

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Problem

Solution:

=

=

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Integrals of some more types

  • Let I =

Solution: Taking constant function 1 as the second function

and integrating by parts, we have

I = x

= x

= x

= x

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= x

= x

= x

Or 2I = x

Or I =

Similarly, integrating other two integrals by parts, taking constant

function 1 as the second functions, we get

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(2)

Hint; Put x = a

(3)

Hint Put x = a

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