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Popular >

integral of 1/(x-3)

Solution

\int \frac{1}{x - 3} d x

Solution

ln ∣ x - 3 ∣ + C

Solution steps

\int \frac{1}{x - 3} 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 - 3

= ln ∣ x - 3 ∣

Add a constant to the solution

= ln ∣ x - 3 ∣ + C

Popular Examples

integral of 5^{cos(3x)}sin(3x)

\int 5^{c o s (3 x)} sin (3 x) d x

derivative of f(x)=9e^x derivative of

f (x) = 9 e^{x}

taylor e^{2x}-x taylor

e^{2 x} - x

10y^{''}-10y^'+125y=0

10 y^{^{''}} - 10 y^{^{'}} + 125 y = 0

limit as x approaches infinity of (1+1/(6x))^{5x}

x \to \infty lim ((1 + \frac{1}{6 x})^{5 x})

Frequently Asked Questions (FAQ)

What is the integral of 1/(x-3) ?
The integral of 1/(x-3) is ln|x-3|+C