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Question
Find the following integrals:
`int (x^3 + 3x + 4)/sqrtx dx`
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Solution
Let I = `int (x^3 + 3x + 4)/sqrtx` dx
`I = int (x^(5/2) + 3x^(1/2) + 4x^(-(1)/2))` dx
`I = int x^(5/2) dx + 3 int x^(1/2) dx + 4 int x^(-(1)/2) dx`
`I = 2/7 x^(7/2) + 3 xx 2/3 x^(5/2) + 4 xx 2x^(1/2) + C`
`I = 2/7 x^(7/2) + 2x^(3/2) + 8 sqrtx + C`
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