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