Evaluate the Integral

Problem

(∫_^)(√(3,x)*d(x))

Solution

1. Rewrite the radical expression as a power using the rule √(n,x^m)=x^m/n

(∫_^)(x^1/3*d(x))

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

(x^(1/3+1))/(1/3+1)+C

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

(x^4/3)/4/3+C

4. Multiply by the reciprocal of the denominator to find the final form.

3/4*x^4/3+C

Final Answer

(∫_^)(√(3,x)*d(x))=(3*x^4/3)/4+C

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