Evaluate the Integral

Problem

(∫_^)(√(9,x)*d(x))

Solution

1. Rewrite the radical expression as a power with a fractional exponent using the rule √(n,x)=x(1/n)

(∫_^)(x(1/9)*d(x))

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

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

3. Simplify the exponent and the denominator by adding the fractions.

(x(10/9))/(10/9)+C

4. Multiply by the reciprocal of the denominator to simplify the expression.

9/10*x(10/9)+C

Final Answer

(∫_^)(√(9,x)*d(x))=9/10*x(10/9)+C

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