integral x/(x+5)^1/2
(u-5)/u^1/2 du giving
u^1/2 du -5u^-1/2 du
and integral will be now
2/3 u^3/2 -10u^1/2 +c
=2/3(x+5)^3/2 -10(x+5)^1/2 +c
=2/3(x+5)^1/2{(x+5) -30} +c
=2/3(x+5)^1/2{(x -25} +c
have i done something wrong??
No, you haven't done anything wrong. Your approach and calculations are correct. However, there is a small mistake in your final expression.
The correct expression for the integral of x/(x+5)^(1/2) is:
2/3(x+5)^(3/2) - 10(x+5)^(1/2) + C
To simplify further, you can factor out (x+5)^(1/2) from both terms, giving:
2/(3√(x+5)) * (x+5) * (x+5) - 10√(x+5) + C
Simplifying this expression gives:
2/3√(x+5) * (x+5)^2 - 10√(x+5) + C
= 2/3(x+5)^(3/2) - 20√(x+5) + C
So, the correct final expression for the integral is:
2/3(x+5)^(3/2) - 20√(x+5) + C