integration of 1/[(x+a)^1/2+(x+b)^1/2]
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Step-by-step explanation:
(x−a)(x−b)=x
2
−(a+b)x+ab=x
2
−(a+b)x+
4
(a+b)
2
−
4
(a+b)
2
+ab
=[x−(
2
a+b
)]
2
−
4
(a−b)
2
⇒∫
(x−a)(x−b)
1
dx=∫
{x−(
2
a+b
)}
2
−(
2
a−b
)
2
1
dx
Let x−(
2
a+b
)=t⇒dx=dt
⇒∫
{x−(
2
a+b
)}
2
−(
2
a−b
)
2
1
dx=∫
t
2
−(
2
a−b
)
2
1
dt
=log
∣
∣
∣
∣
∣
∣
∣
t+
t
2
−(
2
a−b
)
2
∣
∣
∣
∣
∣
∣
∣
+C
=log
∣
∣
∣
∣
∣
{x−(
2
a+b
)}+
(x−a)(x−b)
∣
∣
∣
∣
∣
+
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