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

The integral of 1/(x*sqrt(x-1)) is 2arctan(sqrt(x-1))+C

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integral of 1/(x*sqrt(x-1))

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

2 arctan (x - 1) + C

Solution steps

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

Apply u-substitution

: \int \frac{2}{u ^{2} + 1} d u

= \int \frac{2}{u ^{2} + 1} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= 2 arctan (u)

Substitute back

u = x - 1

= 2 arctan (x - 1)

Add a constant to the solution

= 2 arctan (x - 1) + C

\frac{\partial}{\partial x} (\frac{x + 4}{y + 4})

x \to 2 lim (3 x^{2} - 7 x)

\int \frac{x ^{2}}{x ^{3} + 4} d x

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

e^{x} (1 + x)^{- 1}

What is the integral of 1/(x*sqrt(x-1)) ?
The integral of 1/(x*sqrt(x-1)) is 2arctan(sqrt(x-1))+C