Evaluate the Integral integral of x^(4/3) with respect to x

Problem

(∫_^)(x(4/3)*d(x))

Solution

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

2. Apply the power rule by adding 1 to the exponent n=4/3

n+1=4/3+3/3=7/3

3. Divide the expression by the new exponent 7/3

(x(7/3))/(7/3)

4. Simplify the fraction by multiplying by the reciprocal of the denominator.

3/7*x(7/3)

5. Add the constant of integration C to complete the indefinite integral.

Final Answer

(∫_^)(x(4/3)*d(x))=(3*x(7/3))/7+C

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