Question

Integrate the following with respect to x.

`sqrt(3x + 5)`

Answer 1

`sqrt(3x + 5) = (3 + 5)^(1/2)`

This is of the form (ax + b)ⁿ where a = 3, b = 5, n = `1/2`

`int  ("a"x + "b")^"n"  "d"x = ("a"x + "b")^("n" + 1)/("a"("n" + 1)) + "c"`

So `int (3x + 5)^(1/2)  "d"x = (3x + 5)^(1/2 + 1)/(3(1/2 + 1))`

= `(3x + 5)^(3/2)/(3(3/2)`

= `(3x + 5)^(3/2)/(9/2) + "c"`

= `2/9 (3x + 5)^(3/2) + "c"`