Question

plzzzzzzzz solve this immediately​

Answer 1

Explanation:

Denominator has square term you can guess there may be

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

For way seeing these kind of hints is only practice more questions