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

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

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integral of 7/(x-1)

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

7 ln ∣ x - 1 ∣ + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 7 ln ∣ u ∣

Substitute back

u = x - 1

= 7 ln ∣ x - 1 ∣

Add a constant to the solution

= 7 ln ∣ x - 1 ∣ + C

\int \frac{2 x - 1}{x ( x - 1 ) ^{2}} d x

\int e^{t y} d y

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + y = 0

\int \frac{x}{x + 7} d x

y^{^{''}} + 4 y = 4 sec (2 t)