What is the integral of 4/(x+3) ?

The integral of 4/(x+3) is 4ln|x+3|+C

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integral of 4/(x+3)

\int \frac{4}{x + 3} d x

4 ln ∣ x + 3 ∣ + C

Solution steps

\int \frac{4}{x + 3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int \frac{1}{x + 3} d x

Apply u-substitution

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

= 4 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 ln ∣ u ∣

Substitute back

u = x + 3

= 4 ln ∣ x + 3 ∣

Add a constant to the solution

= 4 ln ∣ x + 3 ∣ + C

f (x) = lo g_{3} (3 x - 6)

\int_{0}^{2} 5 t^{9} d t

\frac{d}{d x} (x^{6} e^{5 x})

x \to 0 lim (\frac{( x ^{2} )}{x - 1})

y = \frac{1}{x ^{3}}, (2, \frac{1}{8})