Evaluate the Integral

Problem

(∫_^)(√(,x11)*d(x))

Solution

1. Rewrite the integrand using a fractional exponent by applying the rule √(n,xm)=x(m/n)

(∫_^)(x(11/2)*d(x))

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

(x(11/2+1))/(11/2+1)+C

3. Simplify the exponent and the denominator by performing the addition 11/2 + 2/2 = 13/2$.

(x(13/2))/(13/2)+C

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

2/13*x(13/2)+C

Final Answer

(∫_^)(√(,x11)*d(x))=(2*x(13/2))/13+C

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