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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

Graph

Popular Examples

integral of (3x)/(sqrt(81+x^2))

\int \frac{3 x}{81 + x ^{2}} d x

integral of 3cos^2(5x)

\int 3 cos^{2} (5 x) d x

integral of (4x^3-2/(x^2)-1)

\int (4 x^{3} - \frac{2}{x ^{2}} - 1) d x

integral of 8e^{2t}

\int 8 e^{2 t} d t

integral of (e^{x^2})/2

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

Frequently Asked Questions (FAQ)

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