Write down the integral of the following
`2x-3 cos x+e^x`

Answer

To find the integral of the expression \(2x - 3 \cos x + e^x\), we will integrate each term separately.

### Step-by-step Solution:

1. **Write down the integral**:
\[ \int (2x - 3 \cos x + e^x) \, dx \]

2. **Apply the linearity of integration**:
We can split the integral into separate integrals:
\[ \int 2x \, dx - 3 \int \cos x \, dx + \int e^x \, dx \]

3. **Integrate each term**:
- For the first term, \( \int 2x \, dx \):
\[ = 2 \cdot \frac{x^2}{2} = x^2 \]
- For the second term, \( -3 \int \cos x \, dx \):
\[ = -3 \cdot \sin x \]
- For the third term, \( \int e^x \, dx \):
\[ = e^x \]

4. **Combine the results**:
Now we combine all the integrated terms:
\[ x^2 - 3 \sin x + e^x + C \]
where \(C\) is the constant of integration.

5. **Final answer**:
Thus, the integral of the given expression is:
\[ \int (2x - 3 \cos x + e^x) \, dx = x^2 - 3 \sin x + e^x + C \]