求不定积分(含根号)哪位高人帮忙解答一下?!∫x(根号(1+x))dx
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求不定积分(含根号)
哪位高人帮忙解答一下?!
∫x(根号(1+x))dx
哪位高人帮忙解答一下?!
∫x(根号(1+x))dx
![求不定积分(含根号)哪位高人帮忙解答一下?!∫x(根号(1+x))dx](/uploads/image/z/12009440-56-0.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%88%E5%90%AB%E6%A0%B9%E5%8F%B7%EF%BC%89%E5%93%AA%E4%BD%8D%E9%AB%98%E4%BA%BA%E5%B8%AE%E5%BF%99%E8%A7%A3%E7%AD%94%E4%B8%80%E4%B8%8B%3F%21%E2%88%ABx%28%E6%A0%B9%E5%8F%B7%281%2Bx%29%29dx)
令 √(1+x) = u, 1+x = u², dx = 2udu
∫x√(1+x)dx
=∫(u²-1)u×2udu
=2∫(u⁴- u²)du
=2[(u^5)/5 - u³/3] + C
=(2/5)[√(1+x)]^5 - ⅔[√(1+x)]³ + C
经验证,答案准确无误.
∫x√(1+x)dx
=∫(u²-1)u×2udu
=2∫(u⁴- u²)du
=2[(u^5)/5 - u³/3] + C
=(2/5)[√(1+x)]^5 - ⅔[√(1+x)]³ + C
经验证,答案准确无误.