_ ^ dx x^2 + 2x + 2 = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{{x^2} + 2x + 2}} = } $

A
${\sin ^{ - 1}}(x + 1) + c$
B
${\sinh ^{ - 1}}(x + 1) + c$
C
${\tanh ^{ - 1}}(x + 1) + c$
✓
${\tan ^{ - 1}}(x + 1) + c$

✓

Answer

Correct option: D.

${\tan ^{ - 1}}(x + 1) + c$

d
(d)$\int_{}^{} {\frac{{dx}}{{{x^2} + 2x + 2}} = \int_{}^{} {\frac{{dx}}{{{{(x + 1)}^2} + 1}} = {{\tan }^{ - 1}}(x + 1) + c} } $.

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