Example 13 - Find integral 3x - 2 / (x + 1)2 (x + 3) dx - Examples

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise

Transcript

Example 13 Find 3 2 + 1 2 + 3 We can write Integral as 3 2 + 1 2 + 3 = + 1 + + 1 2 + + 3 3 2 + 1 2 + 3 = + 1 + 3 + + 3 + + 1 2 + 1 2 + 3 By cancelling denominator 3 2= +1 +3 + +3 + +1 2 Putting x = 1 3 1 2= 1+1 1+3 + 1+3 + 1+1 2 3 2= 0+ 2+ 0 2 5= 2 = 5 2 Similarly putting x = 3 3 3 2= 3+1 3+3 + 3+3 + 3+1 2 9 2= 0+ 0+ 2 2 11=0+0+ 4 11=4 11 4 = = 11 4 Now, Putting x = 0 3(0) 2 = A(1) (3) + B(3) + C (1) 2 2 = 3A + 3B + C Putting value of B & C 2 = 3A + 3 5 2 + 11 4 2 = 3A 15 2 11 4 2 = 3A + 30 11 4 8 = 12A 41 41 8 = 12A 33 12 = A 11 4 = A Hence we can write 3 2 + 1 2 + 3 = 11 4 + 1 5 2 + 1 2 11 4 + 3 Therefore 3 2 + 1 2 + 3 = 11 4 + 1 5 2 + 1 2 11 4 + 3 = 11 4 log +1 5 2 1 + 1 11 4 log +3 + = 11 4 log +1 log +3 + 5 2 + 1 + = + + + + +

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