Question
$\int {\cfrac{{dx}}{{{x^2} + 2x + 2}}}$ equals
- (a) $x{\tan ^{ - 1}}\left( {x + 1} \right) + C$
- (b) ${\tan ^{ - 1}}\left( {x + 1} \right) + C$
- (c) $\left( {x + 1} \right){\tan ^{ - 1}}x + C$
- (d) ${\tan ^{ - 1}}x + C$
Integrals — Class 12 Maths Solution
Step-by-step Solution
Option b is correct
Let $I = \int {\cfrac{{dx}}{{{x^2} + 2x + 2}}} = \int {\cfrac{{dx}}{{{{\left( {x + 1} \right)}^2} + 1}}} = {\tan ^{ - 1}}\left( {x + 1} \right) + C$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.