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Evaluate int ((8x+13)/sqrt(4x+7)) dx (A)...

Evaluate `int ((8x+13)/sqrt(4x+7)) dx` (A) `1/3 (4x+7)^(3/2) - 1/2 (4x+7)^(1/2) + c` (B) `1/6 (4x+7)^(5/2) - 2/3 (4x+7)^(3/2) + c` (C) `1/3 (4x+7)^(5/2) - 1/2 (4x+7)^(3/2) + c` (D) `(4x+7)^(3/2) - 1/2 (4x+7)^(1/2) + c`

Text Solution

Verified by Experts

`int(8x+13)/(sqrt(4x+7))dx=int(8x+14-1)/(sqrt(4x+7))dx`
`=int(2(4x+7)-1)/(sqrt(4x+7))dx`
`=2 intsqrt(4x+7)dx-int(1)/(sqrt(4x+7))dx`
`=2{((4x+7)^(3//2))/(4xx(3)/(2))}-{((4x+7)^(1//2))/(4xx(1)/(2))}+C`
`=(1)/(3)(4x+7)^(3//2)-(1)/(2)(4x+7)^(1//2)+C`
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