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Find the following indefinite integrals: ∫ (1 + 2x) / [x (x + 1)] DX and ∫ 1 / (X & # 178; - X-6) DX
Let (1 + 2x) / [x (x + 1)] = A / x + B / (x + 1) let x = 0, a = (1 + 0) / (0 + 1) = 1, let x = - 1, B = (1 - 2) / (- 1) = 1 (1 + 2x) / [x (x + 1)] = 1 / x + 1 / (x + 1) ∫ (1 + 2x) / [x (x + 1)] DX = ∫ 1 / X DX + ∫ 1 / (1 + x) DX = LN |
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