What is the integral of 1/(10(x+2)) ?

The integral of 1/(10(x+2)) is 1/10 ln|x+2|+C

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integral of 1/(10(x+2))

\int \frac{1}{10 ( x + 2 )} d x

\frac{1}{10} ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{1}{10 ( x + 2 )} d x

Take the constant out:

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

= \frac{1}{10} \cdot \int \frac{1}{x + 2} d x

Apply u-substitution

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

= \frac{1}{10} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} ln ∣ u ∣

Substitute back

u = x + 2

= \frac{1}{10} ln ∣ x + 2 ∣

Add a constant to the solution

= \frac{1}{10} ln ∣ x + 2 ∣ + C

\int 4 cot^{3} (x) csc^{3} (x) d x

y = 5 2 x^{3} + 8 x, (2, 2)

x \to 0 lim (\frac{sin ( 0 )}{0})

x^{3} - 3 x^{2} - 9 x + 27, x + 3

x \to 2 lim (x^{2} + 2 x + 3)

What is the integral of 1/(10(x+2)) ?
The integral of 1/(10(x+2)) is 1/10 ln|x+2|+C