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Integrate the Functions (X^2 + X + 1)/((X + 1)^2 (X + 2)) - CBSE (Commerce) Class 12 - Mathematics

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Question

Integrate the functions `(x^2 + x + 1)/((x + 1)^2 (x + 2))`

Solution

Equating the coefficients of x2x,and constant term, we obtain

A + C = 1

3A + B + 2= 1

2A + 2B + C = 1

On solving these equations, we obtain

A = −2, B = 1, and C = 3

From equation (1), we obtain

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Solution Integrate the Functions (X^2 + X + 1)/((X + 1)^2 (X + 2)) Concept: Integration as an Inverse Process of Differentiation.
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