integration of x power 2/5
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Answered by
1
Answer:
I=∫x
5
⋅
a
3
+x
3
dx
=∫x
3
⋅x
2
a
3
+x
3
dx
Put a
2
+x
3
=t
2
∴t=(a
4
+x
3
)
2
1
⇒3x
2
dx=2tdt
⇒x
2
dx=
3
2t
dt
=∫(t
2
−a
3
)⋅
3
2t
⋅tdt
=∫(t
2
−a
3
)
3
2t
2
dt
=
3
2
∫(t
4
−t
2
a
3
)dt
=
3
2
[
5
t
5
−
3
t
3
a
3
]+c
=
3
2
⎣
⎢
⎢
⎢
⎢
⎡
5
(a
3
+x
3
)
2
5
−
3
a
3
(a
3
+x
3
)
2
3
⎦
⎥
⎥
⎥
⎥
⎤
+c
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