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Popular >

integral of 1-ln(x)

Solution

\int 1 - ln (x) d x

Solution

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

Popular Examples

integral of x^7sqrt(x^4+6)

\int x^{7} x^{4} + 6 d x

derivative of (x^3-sec(3x^2-4))^{-3}derivative of

(x^{3} - sec (3 x^{2} - 4))^{- 3}

derivative of 2/(sqrt(x)-1)

\frac{d}{d x} (\frac{2}{x} - 1)

y^{''}+3y^'+2y=0,y(1)=1,y^'(1)=0

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y (1) = 1, y^{^{'}} (1) = 0

derivative of-8/(x^2)-8/(x^3)derivative of

- \frac{8}{x ^{2}} - \frac{8}{x ^{3}}

Frequently Asked Questions (FAQ)

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