7
4
x
(1-x) 4
dae
1 + x²
Answers
Answered by
0
Answer:
Step-by-step explanation:
I=∫
x
4
+7x
2
+1
(x
2
+1)dx
I=∫
x
2
(x
2
+7+
x
2
1
)
x
2
(1+
x
2
1
)dx
I=∫
(x
2
+7+
x
2
1
)
(1+
x
2
1
)dx
I=∫
(x
2
+
x
2
1
+7)
(1+
x
2
1
)dx
I=∫
(x
2
+
x
2
1
−2x
2
×
x
2
1
+2x
2
×
x
2
1
+7)
(1+
x
2
1
)dx
⇒I=∫
(x−
x
1
)
2
+9
(1+
x
2
1
)dx
Let t=x−
x
1
⇒dt=(1+
x
2
1
)dx
⇒I=∫
t
2
+9
dt
=
3
1
tan
−1
(
3
t
)+c
=
3
1
tan
−1
⎝
⎜
⎜
⎛
3
x−
x
1
⎠
⎟
⎟
⎞
+c where t=x−
x
1
=
3
1
tan
−1
(
3x
x
2
−1
)+c
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