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Popular >

integral of 1-1/(x+1)

Solution

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

Solution

x - ln ∣ x + 1 ∣ + C

Solution steps

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

\int 1 d x = x

\int \frac{1}{x + 1} d x = ln ∣ x + 1 ∣

= x - ln ∣ x + 1 ∣

Add a constant to the solution

= x - ln ∣ x + 1 ∣ + C

Popular Examples

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

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

integral of (x-1/x)^2

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

y^'=(x-5)e^{-2y}

y^{^{'}} = (x - 5) e^{- 2 y}

integral from 1 to 2 of (v^4+5v^7)/(v^3)

\int_{1}^{2} \frac{v ^{4} + 5 v ^{7}}{v ^{3}} d v

laplacetransform-t^2\delta(t-2)laplace transform

- t^{2} δ (t - 2)

Frequently Asked Questions (FAQ)

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