Find the general indefinite integral. (Use C for the constant of integration.)



(5x + cos(x)) dx

1 answer

To find the indefinite integral of \( (5x + \cos(x)) , dx \), we can break it down into two separate integrals:

\[ \int (5x + \cos(x)) , dx = \int 5x , dx + \int \cos(x) , dx \]

Now, we will compute each integral separately.

  1. Integral of \( 5x \): \[ \int 5x , dx = 5 \cdot \frac{x^2}{2} = \frac{5x^2}{2} \]

  2. Integral of \( \cos(x) \): \[ \int \cos(x) , dx = \sin(x) \]

Now, we can combine the results:

\[ \int (5x + \cos(x)) , dx = \frac{5x^2}{2} + \sin(x) + C \]

where \( C \) is the constant of integration.

Thus, the final result is:

\[ \int (5x + \cos(x)) , dx = \frac{5x^2}{2} + \sin(x) + C \]