write the degree of the polynomial x + 9
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In order to evaluate this type of Integrals, we may follow the following algorithm.
STEP I Check whether degree of P(x)≥ or <n.
STEP II If degree of p(x)<n, express P(x) in the from
A
0
+A
1
(ax+b)+A
2
(ax+b)
2
+....+A
n−1
(ax+b)
n−1
STEP III Write
(ax+b)
2
P(x)
as
(ax+b)
n
A
0
+
(ax+b)
n−1
A
1
+
(ax+b)
n−2
A
2
+....+
ax+b
A
n−1
STEP IV Evaluate
∫
(ax+b)
n
Px
dx=A
0
∫
(ax+b)
n
1
dx+A
1
∫
(ax+b)
n−1
1
dx+....+A
n−1
∫
ax+b
1
dx
STEP V If degree of P(x)≥n, then divide P(x) by (ax+b)
n
and express
(ax+b)
n
P(x)
as Q(x)+
(ax+b)
n
R(x)
, where degree of R(x) is less than n.
STEP VI Use step II and III to evaluate ∫
(ax+b)
n
R(x)
dx
Medium
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