Evaluate the Integral

Problem

(∫_^)(3√(3,x2)*d(x))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(3,x2)=x(2/3)

2. Substitute the exponential form back into the integral.

(∫_^)(3*x(2/3)*d(x))

3. Apply the constant multiple rule to move the constant outside the integral.

3*(∫_^)(x(2/3)*d(x))

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

3⋅(x(2/3+1))/(2/3+1)+C

5. Simplify the exponent and the denominator.

3⋅(x(5/3))/(5/3)+C

6. Multiply by the reciprocal of the denominator to simplify the expression.

3⋅3/5*x(5/3)+C

7. Calculate the final coefficient.

9/5*x(5/3)+C

Final Answer

(∫_^)(3√(3,x2)*d(x))=9/5*x(5/3)+C

Want more problems? Check here!