Solution:Multiply the numerator and denominator of the fraction by
sqrt(ax) giving
sqrt(ax) / ( (1+sqrt(ax)) (sqrt(ax)) )
And then express sqrt(ax) as 1+sqrt(ax) - 1, and split the fraction
into two so our original integral becomes
òdx/sqrt(ax) - òdx/(
(1+sqrt(ax)) (sqrt(ax)) )
Then the first integral is just (2/a) sqrt(ax), and the second can be
solved using the substitution
u = 1 + sqrt(ax), so
du = (a/2) (dx / sqrt(ax)), and
(2/a) du = dx/sqrt(ax)
That way, our second integral becomes
(2/a) ò du/u
So the second integral is (2/a) ln(u) = (2/a) ln(1+sqrt(ax))
