Solve the following differential equation: `(dy)/(dx)=cos^3xsin^2x+xsqrt(2x-1)`

Explanation

To solve the differential equation \(\frac{dy}{dx} = \cos^3 x \sin^2 x + x \sqrt{2x - 1}\), we will integrate both sides step by step.

### Step 1: Set up the integral
We start with the equation:
\[ \frac{dy}{dx} = \cos^3 x \sin^2 x + x \sqrt{2x - 1} \]
To find \(y\), we integrate both sides with respect to \(x\):
...