# Evaluate: ∫dx/(3-2x-x^2) - Mathematics and Statistics

Sum

Evaluate: int "dx"/(3 - 2"x" - "x"^2)

#### Solution

Let I = int "dx"/(3 - 2"x" - "x"^2)

3 - 2x - x2 = - x2 - 2x + 3

= -(x2 + 2x - 3)

= - (x2 + 2x + 1 - 4)

= - [(x + 1)2 - 4]

= (2)2 - (x + 1)2

∴ I = int "dx"/((2)^2 - ("x + 1")^2)

= 1/(2(2)) log |(2 + "x" + 1)/(2 - ("x + 1"))| + c

∴ I = 1/4 log |(3 + "x")/(1 - "x")| + c

Concept: Methods of Integration: Integration by Parts
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 4.3 | Page 138