What is the integral of (6000)/(6x+70) ?

The integral of (6000)/(6x+70) is 1000ln|6x+70|+C

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integral of (6000)/(6x+70)

\int \frac{6000}{6 x + 70} d x

1000 ln ∣ 6 x + 70 ∣ + C

Solution steps

\int \frac{6000}{6 x + 70} d x

Take the constant out:

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

= 6000 \cdot \int \frac{1}{6 x + 70} d x

Apply u-substitution

= 6000 \cdot \int \frac{1}{6 u} d u

Take the constant out:

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

= 6000 \cdot \frac{1}{6} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 6000 \cdot \frac{1}{6} ln ∣ u ∣

Substitute back

u = 6 x + 70

= 6000 \cdot \frac{1}{6} ln ∣ 6 x + 70 ∣

Simplify

6000 \cdot \frac{1}{6} ln ∣ 6 x + 70 ∣ : 1000 ln ∣ 6 x + 70 ∣

= 1000 ln ∣ 6 x + 70 ∣

Add a constant to the solution

= 1000 ln ∣ 6 x + 70 ∣ + C

d er i v a t i v e y = \frac{x}{x + \frac{b}{x}}

t a y l or \frac{1}{( 1 + x ) ^{3}}, 0

in v erse l a pl a ce \frac{3}{s ^{2} + 9}

t an g e n t h (x) = \frac{9}{x}, at x = 2

t a y l or e^{- 5 x - 3}, 5

What is the integral of (6000)/(6x+70) ?
The integral of (6000)/(6x+70) is 1000ln|6x+70|+C