Evaluate the Integral

Problem

(∫_^)(1/√(,1−x2)*d(x))

Solution

1. Identify the integrand as a standard form from the table of basic integrals.

2. Recognize that the derivative of the inverse sine function, arcsin(x) is exactly 1/√(,1−x2)

3. Apply the rule for the antiderivative of this specific algebraic form.

4. Add the constant of integration C because this is an indefinite integral.

Final Answer

(∫_^)(1/√(,1−x2)*d(x))=arcsin(x)+C

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