What is the integral of 1/(5-7x) ?

The integral of 1/(5-7x) is -1/7 ln|5-7x|+C

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integral of 1/(5-7x)

\int \frac{1}{5 - 7 x} d x

- \frac{1}{7} ln ∣ 5 - 7 x ∣ + C

Solution steps

\int \frac{1}{5 - 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 = 5 - 7 x

= - \frac{1}{7} ln ∣ 5 - 7 x ∣

Add a constant to the solution

= - \frac{1}{7} ln ∣ 5 - 7 x ∣ + C

y^{^{''''}} + 4 y^{^{''}} + 4 y = 0

\frac{\partial}{\partial x} (2 x y^{2} - 2 x^{3} y)

n = 0 \sum \infty \frac{( ( 1 ) ^{n} )}{n}

y = \frac{x ^{2} + 1}{2 x ^{2} - 1}

\frac{d}{d x} (1 - cos (x - 1))