(x^2+9)分之5x^3dx 的不定积分是多少,
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(x^2+9)分之5x^3dx 的不定积分是多少,
![(x^2+9)分之5x^3dx 的不定积分是多少,](/uploads/image/z/19881267-51-7.jpg?t=%28x%5E2%2B9%29%E5%88%86%E4%B9%8B5x%5E3dx+%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E6%98%AF%E5%A4%9A%E5%B0%91%2C)
∫ 5x³/(x²+9) dx
=∫ 5x²/(x²+9) xdx
=5/2 ∫ x²/(x²+9) dx²
=5/2 ∫ (x²+9-9)/(x²+9) dx²
=5/2 ∫ [1-9/(x²+9)] dx²
=5/2 [ x² - ∫ 9/(x²+9) dx²]
=5/2 [ x² - 9ln(x²+9) ]
=∫ 5x²/(x²+9) xdx
=5/2 ∫ x²/(x²+9) dx²
=5/2 ∫ (x²+9-9)/(x²+9) dx²
=5/2 ∫ [1-9/(x²+9)] dx²
=5/2 [ x² - ∫ 9/(x²+9) dx²]
=5/2 [ x² - 9ln(x²+9) ]