What is the integral of 1/(7-7x) ?

The integral of 1/(7-7x) is -1/7 ln|7-7x|+C

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integral of 1/(7-7x)

\int \frac{1}{7 - 7 x} d x

- \frac{1}{7} ln ∣ 7 - 7 x ∣ + C

Solution steps

\int \frac{1}{7 - 7 x} d x

Apply u-substitution

: \int - \frac{1}{7 u} d u

= \int - \frac{1}{7 u} d u

Take the constant out:

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

= - \frac{1}{7} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{7} ln ∣ u ∣

Substitute back

u = 7 - 7 x

= - \frac{1}{7} ln ∣ 7 - 7 x ∣

Add a constant to the solution

= - \frac{1}{7} ln ∣ 7 - 7 x ∣ + C

\int \frac{x ^{2} + x + 2}{x ^{4} + 5 x ^{2} + 4} d x

\int 6 x^{5} - 8 x^{4} - 9 x^{2} d x

y^{^{'}} = 2 t e^{7 y}

\int x e^{- 4 x} d x

f (x) = \frac{- 3}{x ^{4}}