Let I = + 2x + 2 dx = ) 2 + 1 I = | ( x + 1 ) + ) 2 + 1 | + C = | ( x + 1 ) + + 2x + 2 | + C

Integrals — Class 12 Maths Solution

ncert exercise SA NCERT,ex.7.4,Q.10,Page 316

Question

$\cfrac{1}{{\sqrt {{x^2} + 2x + 2} }}$

Step-by-step Solution

Let $I = \int {\cfrac{1}{{\sqrt {{x^2} + 2x + 2} }}} dx = \int {\cfrac{{dx}}{{\sqrt {{{\left( {x + 1} \right)}^2} + 1} }}}$
$\Rightarrow$

$I = \log \left| {\left( {x + 1} \right) + \sqrt {{{\left( {x + 1} \right)}^2} + 1} } \right| + C$

$= \log \left| {\left( {x + 1} \right) + \sqrt {{x^2} + 2x + 2} } \right| + C$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.