Option a is correct Let I = dx = 2 + 2 | x + | + C

Integrals — Class 12 Maths Solution

ncert exercise SA NCERT,ex.7.7,Q.10,Page 330

Question

$\int {\sqrt {1 + {x^2}} dx}$ is equal to

(a) $\cfrac{x}{2}\sqrt {1 + {x^2}} + \cfrac{1}{2}\log \left| {\left( {x + \sqrt {1 + {x^2}} } \right)} \right| + C$
(b) $\cfrac{2}{3}{\left( {1 + {x^2}} \right)^{3/2}} + C$
(c) $\cfrac{2}{3}x{\left( {1 + {x^2}} \right)^{3/2}} + C$
(d) $\cfrac{{{x^2}}}{2}\sqrt {1 + {x^2}} + \cfrac{1}{2}{x^2}\log \left| {x + \sqrt {1 + {x^2}} } \right| + C$

Step-by-step Solution

Option a is correct

Let $I = \int {\sqrt {1 + {x^2}} dx}$

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

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