Evaluate the Integral integral of (x^3)/3 with respect to x

Problem

(∫_^)((x3)/3*d(x))

Solution

1. Identify the constant factor in the integrand. The expression (x3)/3 can be written as 1/3⋅x3

2. Apply the constant multiple rule for integration, which allows the constant 1/3 to be moved outside the integral sign.

1/3*(∫_^)(x3*d(x))

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

1/3⋅(x(3+1))/(3+1)+C

4. Simplify the exponents and the denominators.

1/3⋅(x4)/4+C

5. Multiply the fractions to find the final expression.

(x4)/12+C

Final Answer

(∫_^)((x3)/3*d(x))=(x4)/12+C

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