Evaluate the Integral integral of x^11 with respect to x

Problem

(∫_^)(x11*d(x))

Solution

1. Identify the form of the integral as a power of x which follows the power rule for integration.

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

3. Substitute n=11 into the formula to get (x(11+1))/(11+1)+C

4. Simplify the exponent and the denominator to obtain the final expression.

Final Answer

(∫_^)(x11*d(x))=(x12)/12+C

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