Q. 19

# Evaluate the following integrals:

Answer :

To Find :

Now, let x - 5 be written as (2x + 1) - and split

Therefore ,

=

=

Now solving,

Let = u dx =

Thus, becomes

Now , = = ) =

=

Now solving,

Now, can be written as

i.e,

Here , let x + = y dx = dy

Therefore, can be written as

Formula Used: = log |x +|+ C

Since is of the form with change in variable.

= log |y +|+ C

= log |y +|+ C

Since , x + = y and dx = dy

= log |(x + ) +|+C

Therefore,

= log |x + +|+C

Now ,

= - log |x + +|+C

Therefore ,

= - log |x + +|+C

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