Evaluate the Integral integral of x^5 with respect to x

Problem

(∫_^)(x5*d(x))

Solution

1. Identify the form of the integral as a power of x which follows the power rule for integration (∫_^)(xn*d(x))=(x(n+1))/(n+1)+C

2. Apply the power rule by incrementing the exponent by 1 and dividing the expression by the new exponent.

3. Substitute n=5 into the formula to get (x(5+1))/(5+1)

4. Simplify the expression to obtain the final result.

5. Add the constant of integration C because this is an indefinite integral.

Final Answer

(∫_^)(x5*d(x))=(x6)/6+C

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