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प्रश्न
Integrate the following with respect to x.
`(8x + 13)/sqrt(4x + 7)`
उत्तर
`int (8x + 13)/sqrt(4x + 7) "d"x = int (8x + 13 + 1 - 1)/sqrt(4x + 7) "d"x`
= `int (2(4x + 7) - 1)/sqrt(4x + 7) "d"x`
= `int ((2(4x + 7))/sqrt(4x + 7) - 1/sqrt(4x + 7)) "d"x`
= `int [2.(4x + 7)^(1/2) - (4x + 7)^((-1)/2)] "d"x`
= `[(2(x + 7)^(1/2 + 1))/((1/2 + 1)(4)) - ((4x + 7)^((-1)/2 + 1))/(((-1)/2 + 1)(4))] + "c"`
= `(2(4x + 7)^(3/2))/((3/2)(4)) - (4x + 7)^(1/2)/((1/2)(4)) + "c"`
= `1/3 (4x + 7)^(3/2) - 1/2 (4x + 7)^(1/2) + "c"`
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