Final Answer
Step-by-step Solution
Specify the solving method
Take the constant $\frac{1}{2}$ out of the integral
Learn how to solve definite integrals problems step by step online.
$\frac{1}{2}\int_{4}^{9}\frac{\left(\sqrt{x}+3\right)^2}{\sqrt{x}}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function ((x^1/2+3)^2)/(2x^1/2) from 4 to 9. Take the constant \frac{1}{2} out of the integral. Rewrite the integrand \frac{\left(\sqrt{x}+3\right)^2}{\sqrt{x}} in expanded form. Expand the integral \int\left(\frac{x}{\sqrt{x}}+6+\frac{9}{\sqrt{x}}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Simplify the fraction by x.