Evaluate the Integral integral of x^4 with respect to x

Problem

(∫_^)(x4*d(x))

Solution

1. Identify the form of the integral as a power function xn where n=4

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=4 into the formula to get the new exponent and the denominator.

4. Simplify the expression by calculating 4 + 1 = 5$.

5. Add the constant of integration C to represent the family of antiderivatives.

Final Answer

(∫_^)(x4*d(x))=(x5)/5+C

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