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Popular >

integral of 1/(x-5)

Solution

\int \frac{1}{x - 5} d x

Solution

ln ∣ x - 5 ∣ + C

Solution steps

\int \frac{1}{x - 5} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - 5

= ln ∣ x - 5 ∣

Add a constant to the solution

= ln ∣ x - 5 ∣ + C

Popular Examples

integral of 1/(sqrt(400-x^2))

\int \frac{1}{400 - x ^{2}} d x

t (x) v^{''} + v^{'} = 0

integral of 3/(xln(5x))

\int \frac{3}{x ln ( 5 x )} d x

y^{10}(dy)/(dx)=-9cos(pix)

y^{10} \frac{d y}{d x} = - 9 cos (π x)

integral of sin^2(θ)cos^3(θ)

\int sin^{2} (θ) cos^{3} (θ) d θ

Frequently Asked Questions (FAQ)

What is the integral of 1/(x-5) ?
The integral of 1/(x-5) is ln|x-5|+C