What is the integral of (ln(x)+3) ?

The integral of (ln(x)+3) is xln(x)+2x+C

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integral of (ln(x)+3)

\int (ln (x) + 3) d x

x ln (x) + 2 x + C

Solution steps

\int ln (x) + 3 d x

Apply Integration By Parts

: x (ln (x) + 3) - \int 1 d x

= x (ln (x) + 3) - \int 1 d x

\int 1 d x = x

= x (ln (x) + 3) - x

Simplify

x (ln (x) + 3) - x : x ln (x) + 2 x

= x ln (x) + 2 x

Add a constant to the solution

= x ln (x) + 2 x + C

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x \to 0 + lim (\frac{1}{sin ( x )})