Solve-this-integral-x-1-1-x-1-1-

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!

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