微积分 求步骤？？？ 谢谢。。
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(x - 2)/(2x² + 2x + 1)²
= 4(x - 2)/(4x² + 4x + 2)²
= (20x² + 24x + 2 - 20x² - 20x - 10)/(4x² + 4x + 2)²
= (20x² + 24x + 2)/(4x² + 4x + 2)² - 5/(4x² + 4x + 2)
∫[-5/(4x² + 4x + 2)]dx = -5∫dx/(4x² + 4x + 2) = -(5/2)∫d(2x + 1)/[(2x + 1)² + 1] = (-5/2)arctan(2x + 1) + c1
(20x² + 24x + 2)/(4x² + 4x + 2)²
= (-20x² - 20x - 10 + 40x² + 44x + 12)/(4x² + 4x + 2)²
= [-5(4x² + 4x + 2) + (5x + 3)(8x + 4)]/(4x² + 4x + 2)²
= [(-5x - 3)'(4x² + 4x + 2) -(-5x - 3)(4x² + 4x + 2)']/(4x² + 4x + 2)²
∫[(20x² + 24x + 2)/(4x² + 4x + 2)²]dx = (-5x - 3)/(4x² + 4x + 2) + c2
原式 = (-5/2)arctan(2x + 1) -(5x + 3)/(4x² + 4x + 2) + C
= 4(x - 2)/(4x² + 4x + 2)²
= (20x² + 24x + 2 - 20x² - 20x - 10)/(4x² + 4x + 2)²
= (20x² + 24x + 2)/(4x² + 4x + 2)² - 5/(4x² + 4x + 2)
∫[-5/(4x² + 4x + 2)]dx = -5∫dx/(4x² + 4x + 2) = -(5/2)∫d(2x + 1)/[(2x + 1)² + 1] = (-5/2)arctan(2x + 1) + c1
(20x² + 24x + 2)/(4x² + 4x + 2)²
= (-20x² - 20x - 10 + 40x² + 44x + 12)/(4x² + 4x + 2)²
= [-5(4x² + 4x + 2) + (5x + 3)(8x + 4)]/(4x² + 4x + 2)²
= [(-5x - 3)'(4x² + 4x + 2) -(-5x - 3)(4x² + 4x + 2)']/(4x² + 4x + 2)²
∫[(20x² + 24x + 2)/(4x² + 4x + 2)²]dx = (-5x - 3)/(4x² + 4x + 2) + c2
原式 = (-5/2)arctan(2x + 1) -(5x + 3)/(4x² + 4x + 2) + C
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