Question

integration of 1/(x+2)^2​

Answer 1

How do I integrate functions of the type 1/(1+x) ^2?

Use integration by substitution. Let 1 + x = u. In that case, du = dx.

Thus, int [1/(1+x)^2] dx = int [1/u^2] du

= int [u^-2] du

= -u^-1 + C

= -1/u + C

= -1/(1+x) + C

where C = any arbitrary constant.

Answer 2

Answer:

$\huge \pink {\frac{1}{(x + 2) {}^{2} }}$

See graph in attachment. ↑↑