What is the integral of 2/(x+3) ?

The integral of 2/(x+3) is 2ln|x+3|+C

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integral of 2/(x+3)

\int \frac{2}{x + 3} d x

2 ln ∣ x + 3 ∣ + C

Solution steps

\int \frac{2}{x + 3} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{x + 3} d x

Apply u-substitution

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

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = x + 3

= 2 ln ∣ x + 3 ∣

Add a constant to the solution

= 2 ln ∣ x + 3 ∣ + C

\frac{d}{d x} (\frac{x ^{2} + 3}{( x - 1 ) ^{3} + ( x + 1 ) ^{3}})

(6, - 5), (2, 3)

f (x) = (\frac{x - 3}{x + 3})^{2}, at x = - 2

y^{^{''}} + 7 y^{^{'}} + 10 y = - 18 t e^{3 t}