Evaluate the integral. \int_{2}^{\infty}\frac{dx}{(x+2)^{2}}

hexacordoK 2021-10-13 Answered
Evaluate the integral.
2dx(x+2)2
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Expert Answer

Laith Petty
Answered 2021-10-14 Author has 103 answers
Step 1
The given improper integral is,
2dx(x+2)2
Step 2
Evaluate the integral using substitution as follows.
2dx(x+2)2=21u2du [Substitute u=x+2]
=2u2du
=[1u]2
=1(+2)+(12+2) [Back substitute u]
=14
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