What is the integral of (ln(x)+cos(x)) ?

The integral of (ln(x)+cos(x)) is xln(x)-x+sin(x)+C

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integral of (ln(x)+cos(x))

\int (ln (x) + cos (x)) d x

x ln (x) - x + sin (x) + C

Solution steps

\int ln (x) + cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int ln (x) d x + \int cos (x) d x

\int ln (x) d x = x ln (x) - x

\int cos (x) d x = sin (x)

= x ln (x) - x + sin (x)

Add a constant to the solution

= x ln (x) - x + sin (x) + C

What is the integral of (ln(x)+cos(x)) ?
The integral of (ln(x)+cos(x)) is xln(x)-x+sin(x)+C