( x + x ) 2 dx is equal to

Option b is correct Let I = ( x + x ) 2 dx = 2 x - 2 x ( x - x ) 2 d x = x + x dx = | ( x + x )| + C

Integrals — Class 12 Maths Solution

ncert misc SA NCERT Misc.,Q.42,Page.353

Question

$\int {\cfrac{{\cos 2x}}{{{{\left( {\sin x + \cos x} \right)}^2}}}} dx$ is equal to

(a) $\cfrac{{ - 1}}{{\sin x + \cos x}} + C$
(b) $\log \left| {\sin x + \cos x} \right| + C$
(c) $\log \left| {\sin x - \cos x} \right| + C$
(d) $\cfrac{1}{{{{\left( {\sin x + \cos x} \right)}^2}}} + C$

Step-by-step Solution

Option b is correct

Let $I = \int {\cfrac{{\cos 2x}}{{{{\left( {\sin x + \cos x} \right)}^2}}}} dx = \int {\cfrac{{{{\cos }^2}x - {{\sin }^2}x}}{{{{\left( {\cos x - \sin x} \right)}^2}}}d} x$

$= \int {\cfrac{{\cos x - \sin x}}{{\cos x + \sin x}}} dx$
$= \log |\left( {\cos x + \sin x} \right)| + C$

← All Integrals solutions Practice tests →

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