Evaluate the Integral

Problem

(∫_^)(9/√(,x)*d(x))

Solution

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

9/√(,x)=9*x(−1/2)

2. Apply the constant multiple rule for integrals by moving the constant outside the integral sign.

9*(∫_^)(x(−1/2)*d(x))

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

9*((x(−1/2+1))/(−1/2+1))+C

4. Simplify the exponent and the denominator.

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

5. Multiply by the reciprocal of the denominator to find the final coefficient.

9⋅2*x(1/2)+C

6. Convert the expression back to radical form.

18√(,x)+C

Final Answer

(∫_^)(9/√(,x)*d(x))=18√(,x)+C

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