Evaluate the integral: dx = S 3x²+14x+3 (x−1)(x+1)² +C

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Evaluate the integral :
S
3x²+14x+3
(x-1)(x+1)²'
dx =
+C
Transcribed Image Text:Evaluate the integral : S 3x²+14x+3 (x-1)(x+1)²' dx = +C
Problem 9) Evaluate the Integral:
3 x ² + 14x + 3√x = A +
2
(X-1) (X+1) ²
A (X-1)(X+1) ²
+
0²-11
с
B
+C
(X-1) (x+1) (x+1)²
LCD= (x-1) (X+) ²
2
(x-1) (x + 1)² + C (x-1)(x+1) ²
(x+1)= 1
B
(x++)
-10
Ө
2
·A (x + 1)² + B (x-1) (x + 1) + C (x-1):
X = 1; 4A = 3 + 14+3 = 4A = 20 = A=5
X=-1; -2C₂-8 = C=4
Y₂0 5+1
5 +1 + B (-1) (1) + 4 (-1) = 3 ! dus²²² +C
5-B - 4 1 1 2 3 -1 > B = -2
dvad
-2+1
S²₁ ²504 + 45 x 4 1/² dx
2
(x-1)
((x+1)
U₂8+1
du z dx
5/n/x-1/-2)x+1/= 4/n/x+1/+c
↓
?
U + C
#
-10t+C
Transcribed Image Text:Problem 9) Evaluate the Integral: 3 x ² + 14x + 3√x = A + 2 (X-1) (X+1) ² A (X-1)(X+1) ² + 0²-11 с B +C (X-1) (x+1) (x+1)² LCD= (x-1) (X+) ² 2 (x-1) (x + 1)² + C (x-1)(x+1) ² (x+1)= 1 B (x++) -10 Ө 2 ·A (x + 1)² + B (x-1) (x + 1) + C (x-1): X = 1; 4A = 3 + 14+3 = 4A = 20 = A=5 X=-1; -2C₂-8 = C=4 Y₂0 5+1 5 +1 + B (-1) (1) + 4 (-1) = 3 ! dus²²² +C 5-B - 4 1 1 2 3 -1 > B = -2 dvad -2+1 S²₁ ²504 + 45 x 4 1/² dx 2 (x-1) ((x+1) U₂8+1 du z dx 5/n/x-1/-2)x+1/= 4/n/x+1/+c ↓ ? U + C # -10t+C
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