Evaluate the Integral

Problem

(∫_^)(√(,x^9)*d(x))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(,x^9)=x^(9/2)

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

(∫_^)(x^(9/2)*d(x))=(x^(9/2+1))/(9/2+1)+C

3. Simplify the exponent and the denominator.

9/2+1=11/2

4. Divide by the fraction by multiplying by its reciprocal.

(x^(11/2))/(11/2)=2/11*x^(11/2)

Final Answer

(∫_^)(√(,x^9)*d(x))=2/11*x^(11/2)+C

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