What is the integral of-7x-3+2/(x-1) ?

The integral of-7x-3+2/(x-1) is -(7x^2)/2-3x+2ln|x-1|+C

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integral of-7x-3+2/(x-1)

\int - 7 x - 3 + \frac{2}{x - 1} d x

- \frac{7 x ^{2}}{2} - 3 x + 2 ln ∣ x - 1 ∣ + C

Solution steps

\int - 7 x - 3 + \frac{2}{x - 1} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 7 x d x - \int 3 d x + \int \frac{2}{x - 1} d x

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 3 d x = 3 x

\int \frac{2}{x - 1} d x = 2 ln ∣ x - 1 ∣

= - \frac{7 x ^{2}}{2} - 3 x + 2 ln ∣ x - 1 ∣

Add a constant to the solution

= - \frac{7 x ^{2}}{2} - 3 x + 2 ln ∣ x - 1 ∣ + C

f (z) = \frac{z - 1}{z + 1}

\int 7 e^{2 x + e^{2 x}} d x

\frac{s ^{2}}{s ^{2} + 9}

\int \frac{2 e ^{2 x}}{e ^{2 x} + 16 e ^{x} + 63} d x

ln (x^{6})

What is the integral of-7x-3+2/(x-1) ?
The integral of-7x-3+2/(x-1) is -(7x^2)/2-3x+2ln|x-1|+C