Find the Integral cube root of x

Problem

(∫_^)(√(3,x)*d(x))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(3,x)=x(1/3)

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

(∫_^)(x(1/3)*d(x))=(x(1/3+1))/(1/3+1)+C

3. Simplify the exponent and the denominator by adding the fractions.

1/3+1=4/3

4. Divide by the fraction by multiplying by its reciprocal.

(x(4/3))/(4/3)=3/4*x(4/3)

Final Answer

(∫_^)(√(3,x)*d(x))=(3*x(4/3))/4+C

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