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int(dx)/(sqrt(9x-4x^2))equals(A) 1/9sin^...

`int(dx)/(sqrt(9x-4x^2))`equals(A) `1/9sin^(-1)((9x-8)/8)+C` (B) `1/2sin^(-1)((8x-9)/9)+C`(C) `1/3sin^(-1)((9x-8)/8)+C` (D) `1/2sin^(-1)((9x-8)/9)+C`

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To solve the integral \( \int \frac{dx}{\sqrt{9x - 4x^2}} \), we will follow these steps: ### Step 1: Rewrite the Integral First, we can rewrite the expression under the square root: \[ 9x - 4x^2 = -4x^2 + 9x = -4\left(x^2 - \frac{9}{4}x\right) \] We can complete the square: ...
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