作业帮求积分(1-x)的平方/根号x.
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/22 06:25:18
求积分(1-x)的平方/根号x.
∫ (1 - x)²/√x dx
= ∫(1 - 2x + x²)/√x dx
= ∫ x^(- 1/2) dx - 2∫ x^(1/2) dx + ∫ x^(3/2) dx
= x^(1 - 1/2)/(1 - 1/2) - 2x^(1 + 1/2)/(1 + 1/2) + x^(1 + 3/2)/(1 + 3/2) + C
= 2√x - 2 * 2/3 * x^(3/2) + 2/5 * x^(5/2) + C
= 2√x - (4/3)x^(3/2) + (2/5)x^(5/2) + C
——————————————————————————————————
幂函数公式是：∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C
= ∫(1 - 2x + x²)/√x dx
= ∫ x^(- 1/2) dx - 2∫ x^(1/2) dx + ∫ x^(3/2) dx
= x^(1 - 1/2)/(1 - 1/2) - 2x^(1 + 1/2)/(1 + 1/2) + x^(1 + 3/2)/(1 + 3/2) + C
= 2√x - 2 * 2/3 * x^(3/2) + 2/5 * x^(5/2) + C
= 2√x - (4/3)x^(3/2) + (2/5)x^(5/2) + C
——————————————————————————————————
幂函数公式是：∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C