Solve this integral : ∫(((√(x+1))−1)/( (√(x+1))+1))


Question and Answers Forum

All Questions Topic List
Differential Equation Questions
Previous in All Question Next in All Question
Previous in Differential Equation Next in Differential Equation
Question Number 168267 by Florian last updated on 07/Apr/22

$S o l v e t h i s i n t e g r a l :$ $\int \frac{\sqrt{x + 1} - 1}{\sqrt{x + 1} + 1}$
	Answered by MJS_new last updated on 07/Apr/22

	$\int \frac{\sqrt{x + 1} - 1}{\sqrt{x + 1} + 1} d x =$ $[t = \sqrt{x + 1} \to d x = 2 t d t]$ $= 2 \int \frac{t (t - 1)}{t + 1} d t = \int (2 t - 4 + \frac{4}{t + 1}) d t =$ $= t^{2} - 4 t + 4 \ln (t + 1) =$ $= x - 4 \sqrt{x + 1} + 4 \ln (1 + \sqrt{x + 1}) + C$
	Commented by Florian last updated on 07/Apr/22

	$G o o d!$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum