Evaluate the Integral

Problem

(∫_^)(1/√(,x)*d(x))

Solution

1. Rewrite the integrand using exponent notation to make it easier to apply the power rule.

1/√(,x)=x(−1/2)

2. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C for n≠−1

(∫_^)(x(−1/2)*d(x))=(x(−1/2+1))/(−1/2+1)+C

3. Simplify the exponent and the denominator.

(x(1/2))/(1/2)+C

4. Multiply by the reciprocal of the denominator to find the final form.

2*x(1/2)+C

5. Convert the expression back into radical notation.

2√(,x)+C

Final Answer

(∫_^)(1/√(,x)*d(x))=2√(,x)+C

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