Integrate with respect to x :
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
(viii) 
(ix)(x – 1) 
(x)x 5 
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 
tan –1 
+ C (ii) 
tan –1 
+ C (iii) 
tan –1 
+ C
(iv) n |x 2 + 3x + 4| – 
tan –1 
+ C (v) x − arctan x + n 
+ C
(vi) n |x + 
| + C (vii) 
+ 2 n |x + 
| + C (viii) 
+ 2 n 
+ C
(ix) – 
– 
(2x + 1) 
– 
sin –1 
+ C
(x) 
(a 3 + x 3 ) 5/2 – 
(a 3 + x 3 ) 3/2 + C
Sol. (i) 
= 
tan –1 
(ii) 
= 
tan –1 
+ C
(iii) 
= 
tan –1 
+ C
(iv) Ι = 
Let 2x + 1 = A 
+ B ⇒ 2x + 1 = A(2x + 3) + B ⇒ A = 1 & B = – 2
⇒ Ι = 
– 
= n 
– 
= n(x 2 + 3x + 4) – 
= n(x 2 + 3x + 4) – 
tan –1 
+ C
(v) Ι = 
= 
= x – tan –1 x – 
= x – tan –1 x – n|x| + 
n (x 2 + 1) + C = x – tan –1 x + n 
+ C
(vi) 
= n 
+ C
(vii) 
= 
+ 
n 
+ C
= 
+ 2 n 
+ C
(viii) 
= 
= 
+ 2 n 
+ C
(ix) 
= 
= 
dx – 
dx
= 
dx – 
dx
= – 
– 
(2x + 1) 
– 
sin –1 
+ C
(x) Ι = 
Put a 3 + x 3 = t 2 ⇒ 3x 2 dx = 2t.dt
⇒ Ι = 
= 
= 
+ C
= 
+ C
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems