Expert Answer to "Evaluate the integral. ∫2∞dx(x+2)2"

hexacordoK

Answered question

2021-10-13

Evaluate the integral.

\int_{2}^{\infty} \frac{d x}{{(x + 2)}^{2}}

Laith Petty

Skilled2021-10-14Added 103 answers

Step 1
The given improper integral is,

\int_{2}^{\infty} \frac{d x}{{(x + 2)}^{2}}

Step 2
Evaluate the integral using substitution as follows.

\int_{2}^{\infty} \frac{d x}{{(x + 2)}^{2}} = \int_{2}^{\infty} \frac{1}{u^{2}} d u

[Substitute u=x+2]

= \int_{2}^{\infty} u^{- 2} d u

= {[\frac{- 1}{u}]}_{2}^{\infty}

= \frac{- 1}{(\infty + 2)} + (\frac{1}{2 + 2})

[Back substitute u]

= \frac{1}{4}

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