求定积分换元法∫4,0 x+2/根号2x+1

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求定积分换元法∫4,0 x+2/根号2x+1
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求定积分换元法∫4,0 x+2/根号2x+1
求定积分换元法∫4,0 x+2/根号2x+1

求定积分换元法∫4,0 x+2/根号2x+1
令u = √(2x + 1),u² = 2x + 1,2u du = 2 dx
∫(0→4) (x + 2)/√(2x + 1) dx
= ∫(1→3) [(u² - 1)/2 + 2]/u * (u du)
= (1/2)∫(1→3) (u² + 3) du
= (1/2)[u³/3 + 3u] |(1→3)
= (1/2)[(27/3) + 9] - (1/2)[1/3 + 3]
= 22/3