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in Integrals calculus by (36.9k points)

Evaluate: ∫ (2x + 3)dx/ (x + 1)(x2 + 4) 

1 Answer

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Best answer

The given integral is 

= 2x + 3 = A(x2 + 4) + Bx (x + 1) + C(x + 1)  

When x = –1, A = 1/5 

and x = 0, 4 A + C = 3 

= C = 3 – 4, A = 3 – 4/5 = 11/5

Also x = 1, 5A + 2B + 2 C = 5

= 2B = 5 – 5A – 2C = 5 – 1 – 22/5 = –2/5

= B = –1/5

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