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Popular >

integral of 1/x-1

Solution

\int \frac{1}{x} - 1 d x

Solution

ln ∣ x ∣ - x + C

Solution steps

\int \frac{1}{x} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1}{x} d x - \int 1 d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int 1 d x = x

= ln ∣ x ∣ - x

Add a constant to the solution

= ln ∣ x ∣ - x + C

Popular Examples

integral of (1-cos^2(x))sin(x)

\int (1 - cos^{2} (x)) sin (x) d x

integral of 11sec^{-2}(xta)n^3x

\int 11 sec^{- 2} (x t a) n^{3} x d x

(\partial)/(\partial x)(ye^x+xe^{-y})

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

taylor 1/((7+x)^2)taylor

\frac{1}{( 7 + x ) ^{2}}

tangent of y=(4x)/(x^2+1),(1,2)tangent of

y = \frac{4 x}{x ^{2} + 1}, (1, 2)

Frequently Asked Questions (FAQ)

What is the integral of 1/x-1 ?
The integral of 1/x-1 is ln|x|-x+C