# How do you find the integral of #int (4x+3)/sqrt(1-x^2)#?

The answer is

We need

Rewrite the integral (we apply linearity)

Putting it all together

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To find the integral of (\int \frac{4x+3}{\sqrt{1-x^2}}) with respect to (x), you can use the substitution method. Let (u = 1 - x^2), then (du = -2x , dx). Rearrange to solve for (dx), giving (dx = -\frac{du}{2x}). Substitute these expressions into the integral. You will end up with (\int \frac{4x+3}{\sqrt{1-x^2}} , dx = \int \frac{4x+3}{\sqrt{u}} \cdot \left(-\frac{du}{2x}\right)). Simplify the expression, integrate with respect to (u), then substitute back (u = 1 - x^2) to find the final answer.

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