Solve the following integration
`int cos x^(@)dx`

Answer

To solve the integral \( \int \cos(x^\circ) \, dx \), we need to convert the angle from degrees to radians, as integration is typically performed in radians. Here's the step-by-step solution:

### Step 1: Convert Degrees to Radians
To convert degrees to radians, we use the conversion factor:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
Thus, we convert \( x^\circ \) to radians:
\[ x^\circ = x \times \frac{\pi}{180} \]

### Step 2: Rewrite the Integral
Now we can rewrite the integral in terms of radians:
\[ \int \cos(x^\circ) \, dx = \int \cos\left(x \times \frac{\pi}{180}\right) \, dx \]

### Step 3: Use Substitution
Let \( u = x \times \frac{\pi}{180} \). Then, the differential \( du \) is:
\[ du = \frac{\pi}{180} \, dx \quad \Rightarrow \quad dx = \frac{180}{\pi} \, du \]
Now, substitute \( u \) and \( dx \) into the integral:
\[ \int \cos\left(u\right) \cdot \frac{180}{\pi} \, du = \frac{180}{\pi} \int \cos(u) \, du \]

### Step 4: Integrate
The integral of \( \cos(u) \) is \( \sin(u) \):
\[ \frac{180}{\pi} \int \cos(u) \, du = \frac{180}{\pi} \sin(u) + C \]

### Step 5: Substitute Back
Now substitute back \( u = x \times \frac{\pi}{180} \):
\[ \frac{180}{\pi} \sin\left(x \times \frac{\pi}{180}\right) + C \]

### Final Answer
Thus, the final result of the integral is:
\[ \int \cos(x^\circ) \, dx = \frac{180}{\pi} \sin\left(x \times \frac{\pi}{180}\right) + C \]