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Popular >

integral of x/((x+1))

Solution

\int \frac{x}{( x + 1 )} d x

Solution

x + 1 - ln ∣ x + 1 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{u - 1}{u} d u

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

Expand

\frac{u - 1}{u} : 1 - \frac{1}{u}

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

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

\int 1 d u = u

\int \frac{1}{u} d u = ln ∣ u ∣

= u - ln ∣ u ∣

Substitute back

u = x + 1

= x + 1 - ln ∣ x + 1 ∣

Add a constant to the solution

= x + 1 - ln ∣ x + 1 ∣ + C

Popular Examples

tangent of f(x)= 4/(x+1),\at x=6 tangent of

f (x) = \frac{4}{x + 1}, at x = 6

integral of 1/(2y-1)

\int \frac{1}{2 y - 1} d y

tangent of y=(x^3+2)(3x^2-4x+2),(1,3)tangent of

y = (x^{3} + 2) (3 x^{2} - 4 x + 2), (1, 3)

tangent of x^2(2.4)tangent of

x^{2} (2.4)

integral of 7x+5

\int 7 x + 5 d x

Frequently Asked Questions (FAQ)

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