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Popular >

integral of 1/(x-2)

Solution

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

Solution

ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{1}{x - 2} 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 - 2

= ln ∣ x - 2 ∣

Add a constant to the solution

= ln ∣ x - 2 ∣ + C

Graph

Popular Examples

integral of 5/(usqrt(u^2-1))

\int \frac{5}{u u ^{2} - 1} d u

derivative of f(t)= 9/(sqrt(t))derivative of

f (t) = \frac{9}{t}

derivative of (x-5/(x^2+1))

\frac{d}{d x} (\frac{x - 5}{x ^{2} + 1})

integral of sin(8x-2)

\int sin (8 x - 2) d x

f^'(x)=6x^2-8x,f(3)=27

f^{^{'}} (x) = 6 x^{2} - 8 x, f (3) = 27

Frequently Asked Questions (FAQ)

What is the integral of 1/(x-2) ?
The integral of 1/(x-2) is ln|x-2|+C