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

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

Popular >

integral of 1/(xsqrt(x-1))

\int \frac{1}{x 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

e^{- \frac{h}{7}}

\frac{d}{d x} (x \cdot e^{- x^{2}})

x \to 0 + lim ((tan (6 x))^{2})

\frac{\partial}{\partial x} (x^{5} + y^{7})

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

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