Evaluate the Integral

Problem

(∫_^)(12*x11−11/(x11)*d(x))

Solution

1. Rewrite the integrand by expressing the fraction with a negative exponent to make it easier to apply the power rule.

(∫_^)(12*x11−11*x(−11)*d(x))

2. Apply the sum rule for integration, which allows the integral of a sum to be evaluated as the sum of the integrals.

(∫_^)(12*x11*d(x))−(∫_^)(11*x(−11)*d(x))

3. Apply the power rule for integration, (∫_^)(xn*d(x))=(x(n+1))/(n+1) to each term.

12⋅(x12)/12−11⋅(x(−10))/(−10)+C

4. Simplify the coefficients and rewrite the negative exponent as a fraction.

x12+11/(10*x10)+C

Final Answer

(∫_^)(12*x11−11/(x11)*d(x))=x12+11/(10*x10)+C

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