Evaluate the Integral

Problem

(∫_^)(√(3,x11)*d(x))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(3,x11)=x11/3

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

(∫_^)(x11/3*d(x))=(x(11/3+1))/(11/3+1)+C

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

11/3+1=11/3+3/3=14/3

4. Substitute the simplified values back into the expression.

(x14/3)/14/3+C

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

(3*x14/3)/14+C

Final Answer

(∫_^)(√(3,x11)*d(x))=(3*x14/3)/14+C

Want more problems? Check here!