What is the integral of (ln(x)+1) ?

The integral of (ln(x)+1) is xln(x)+C

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integral of (ln(x)+1)

\int (ln (x) + 1) d x

x ln (x) + C

Solution steps

\int ln (x) + 1 d x

Apply Integration By Parts

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

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

\int 1 d x = x

= x (ln (x) + 1) - x

Simplify

x (ln (x) + 1) - x : x ln (x)

= x ln (x)

Add a constant to the solution

= x ln (x) + C

\frac{d}{d x} ((6 x)^{4 x})

\int \frac{1}{( 5 x - 2 ) ^{\frac{5}{2}}} d x

\frac{\partial}{\partial x} (\frac{2}{x ^{2} + y ^{2}})

(y^{3} - 1) e^{x} d x + 3 y^{2} (e^{x} + 1) d y = 0

(2, - 7), (- 5, 2)