Question

integral e^x(x+2)/(x+3)^2​

Answer 1

Step-by-step explanation:

we have,

$\int {e}^{x} \frac{x + 2}{(x + 3)^{2} } dx$

$\int {e}^{x} \frac{(x + 3 - 1)}{ {(x + 3)}^{2} } dx$

$\int {e}^{x} ( \frac{1}{x + 3} - \frac{1}{(x + 3)^{2} } )dx$

Now, we know that,

$\int {e}^{x}( f(x) + \frac{d(f(x))}{dx}) \\ = {e}^{x} f(x)$

$= \frac{ {e}^{x} }{x + 3} + c$