Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If I = 
, then I equals
A
log 
+ 
log 
+ 
tan –1 
+ C
B
log 
+ 
log 
+ 
tan –1 
+ C
C
log 
+ sin –1 
+ C
D
log 
+ sin –1 
+ 
tan –1 where t = sin x – cos x and b = 5 1/4 
+ C
Text Solution
Verified by ExpertsThe correct answer is:
A
cos 5 x + sin 5 x = (cos x + sin x) [cos 4 x –cos 3 x sin x + cos 2 x sin 2 x –cos x sin 3 x + sin 4 x]
= (cos x + sin x) [(cos 2 x + sin 2 x) 2 – cos 2 x sin 2 x – cos x sin x (cos 2 x + sin 2 x)]
= (cos x + sin x) (1 –cos x sin x – cos 2 x sin 2 x)
∴ I = 
dx
Put sin x – cos x = t, so that (cos x + sin x) dx = dt, and t 2 = 1 –2 sin x cos x
Thus
I = 
= 4 
4 
dt
= 
log 
log 
+ 
tan –1 
+ C
where t = sin x – cos x
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