What is the integral of 1/(2sqrt(x-1)) ?

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

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integral of 1/(2sqrt(x-1))

\int \frac{1}{2 x - 1} d x

x - 1 + C

Solution steps

\int \frac{1}{2 x - 1} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{x - 1} d x

Apply u-substitution

: \int 2 d u

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

Integral of a constant:

\int a d x = a x

= \frac{1}{2} \cdot 2 u

Substitute back

u = x - 1

= \frac{1}{2} \cdot 2 x - 1

Simplify

\frac{1}{2} \cdot 2 x - 1 : x - 1

= x - 1

Add a constant to the solution

= x - 1 + C

y^{^{''}} + 16 y = 8 tan (4 x)

\frac{2 y ^{^{'}}}{y} = x

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

y^{^{''}} + 4 y = - 3 x^{2} + 2 x + 3

x \to 0 lim (\frac{e ^{x} - 1}{x})

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