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

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

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integral of 1/(10x+1)

\int \frac{1}{10 x + 1} d x

\frac{1}{10} ln ∣ 10 x + 1 ∣ + C

Solution steps

\int \frac{1}{10 x + 1} d x

Apply u-substitution

: \int \frac{1}{10 u} d u

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

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}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} ln ∣ u ∣

Substitute back

u = 10 x + 1

= \frac{1}{10} ln ∣ 10 x + 1 ∣

Add a constant to the solution

= \frac{1}{10} ln ∣ 10 x + 1 ∣ + C

\frac{d y}{d x} = y - x

F (C) = \frac{9}{5} C + 32

(2 x - 3 y) d x + (2 y - 3 x) d y = 0

\frac{d}{d x} (x^{2})

\frac{d}{d x} (arctan (4 x^{2} + 1))

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