Question

Integration one upon root x + a + root x + b DX

Answer 1

Answer:

2/3(a-b) [ (x+a)^3/2 + x+b)^3/2 ] + k

Step-by-step explanation:

= $1/ [ (√x+a) + √(x+b) ]

= $ √(x+a) - √(x+b)/( √x+a) + √(x+b)√(x+a) - √(x+b)

$(x+a) - √(x+b)/(a - b)

= 1/(a-b) $[√(x+a)] - $[(√x+b)]

= 1/(a-b) 2/3 [ (x+a)^3/2 + x+b)^3/2 ] + k

= 2/3(a-b) [ (x+a)^3/2 + x+b)^3/2 ] + k

Note : rationalise and then integrate