Question

integration of dx/x^1/2(5-x)^1/2​

Answer 1

integration of dx/x^1/2(5-x)^1/2. Asked by Balbir | 5th Oct, 2017, 12:11: PM. Expert Answer: begin mathsize 16px style integral fraction numerator dx over denominator square root of straight x open ...

Answer 2

Answer:- - 1/2root5x^3/2 +1/10(5-x)^3/2

Step-by-step explanation:Given

dx/root x(5-x) is differentiated bt after sperating it by partial method

The method is as follow

1/root x(5-x)=A/root x +B/root(5-x).......... 1eqn

1=A root(5-x)+B root x

On taking root(5-x)=0

Gives x=root 5

Putting value in eqn give

1=B(root(root5)

B=1/5

Putting rootx x =0

Gives A=1/root 5

Putting the value of A and B in eqn 1

1/root 5x+1/5root(5-x)

Now differentiating

=dx/root 5x +dx/5 root(5-x)]

=1/root 5(-1/2x^3/2) + 1/5(-1/2)(-1/(5-x)^3/2)

= - 1/2root5 x^3/2 + 1/10(5-x)^3/2