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

The integral of (1-ln(x)) is 2x-xln(x)+C

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integral of (1-ln(x))

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

2 x - x ln (x) + C

Solution steps

\int 1 - ln (x) d x

Apply Integration By Parts

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

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

\int - 1 d x = - x

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

Simplify

x (1 - ln (x)) - (- x) : 2 x - x ln (x)

= 2 x - x ln (x)

Add a constant to the solution

= 2 x - x ln (x) + C

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

y^{^{''}} + 2 y^{^{'}} + y = 1, y (1) = 1, y^{^{'}} (1) = 0

x \to - 5 + lim (\frac{( x - 5 )}{x + 5})

\frac{d}{d x} ((6 x + 12)^{3})

\int \frac{x ^{2} + 2 x + 2}{x + 2} d x