Integrate with respect to x :
(i) 
(ii) 
(iii) 
(iv) 
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) n 
+ C (ii) 
n 
– 
tan –1 (t) + C, where t = 
(iii) – 
n 
+ C, where t = 
(iv) – tan –1 
+ C
Sol. (i) Ι = 
Put x + 2 = t 2 ⇒ dx = 2t dt
⇒ Ι = 
= 2. 
n 
+ C = n 
+ C
(ii) Ι = 
put x + 1 = t 2 dx = 2t dt
⇒ Ι = 
(By partial fraction)
= 
dt – 
dt = 
n 
– 
tan –1 t + C, where t = 
(iii) Ι = 
Put x + 1 = 
⇒ dx = – 
dt
⇒ Ι = 
= – 
= – 
= – 
= – 
n 
+ C where t = 
(iv) Ι = 
Put x = 
⇒ dx = – 
dt
⇒ Ι = 
= – 
Again put 1 + 2t 2 = z 2 ⇒ 4t dt = 2z dz
⇒ Ι = – 
= – 
= – tan –1 (z) + C = tan –1 
+ C
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