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Question Number 206543 by luciferit last updated on 18/Apr/24

	Answered by lepuissantcedricjunior last updated on 18/Apr/24
	$∫((3+2(√x))/(4+(√x)))dx=∫((2(4+(√x))−5)/(4+(√x)))dx =2x−{5∫(dx/(4+(√x))) x=t^2 ⇔dx=2tdt} =2x−{10∫(1−(4/(4+t)))dt} =2x−10(√x)+40ln(4+(√x))+c$
	$\int \frac{3 + 2 \sqrt{x}}{4 + \sqrt{x}} d x = \int \frac{2 (4 + \sqrt{x}) - 5}{4 + \sqrt{x}} d x$ $= 2 x - {5 \int \frac{d x}{4 + \sqrt{x}} x = t^{2} \Leftrightarrow d x = 2 t d t}$ $= 2 x - {10 \int (1 - \frac{4}{4 + t}) d t}$ $= 2 x - 10 \sqrt{x} + 40 l n (4 + \sqrt{x}) + c$
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