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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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

\int \frac{x}{3} d x

x \to \infty lim (2 x^{2} - 1)

y^{^{'}} = y (x y^{3} + 1)

\frac{2}{x ^{2}}

\frac{d}{d x} ((x)^{2})