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Popular >

integral of 1/(x-b)

Solution

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

Solution

ln ∣ x - b ∣ + C

Solution steps

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

= ln ∣ x - b ∣

Add a constant to the solution

= ln ∣ x - b ∣ + C

Popular Examples

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\int sin (2 x) d x

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

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\int \frac{1}{x ^{4} + 2 x ^{3} + x ^{2}} d x

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\int e^{c o s^{2} (x)} sin (x) cos (x) d x

integral of (x/(1+x^8))^7

\int (\frac{x}{1 + x ^{8}})^{7} d x

Frequently Asked Questions (FAQ)

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