Evaluate the Integral

Problem

(∫_^)(√(4,x3)*d(x))

Solution

1. Rewrite the radical expression using a fractional exponent. The fourth root of x3 is equivalent to x raised to the power of 3/4

(∫_^)(x3/4*d(x))

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

(x(3/4+1))/(3/4+1)+C

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

(x7/4)/7/4+C

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

4/7*x7/4+C

Final Answer

(∫_^)(√(4,x3)*d(x))=4/7*x7/4+C

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