5 1
Evaluate:
S
2^x+5/x-1/x^1/3
dx
Answers
Answered by
0
Answer:
Step-by-step explanation:
Let I=∫
(x+1)
3
(x−1)e
x
dx
⇒I=∫{
(x+1)
3
x+1−2
}e
x
dx
=∫{
(x+1)
2
1
−
(x+1)
3
2
}e
x
dx
=∫e
x
⋅
(x+1)
2
1
dx−2∫e
x
(x+1)
3
1
dx
Applying integrating by parts, we get
=(
(x+1)
2
1
e
x
−∫e
x
(x+1)
3
(−2)
dx)−2∫e
x
(x+1)
3
1
dx
=
(x+1)
2
e
x
+C
Note We can use the formula
∫e
x
[f(x)+f
′
(x)]dx=e
x
f(x)+C
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