What is the integral of 1/(sqrt(x-5)) ?

The integral of 1/(sqrt(x-5)) is 2sqrt(x-5)+C

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integral of 1/(sqrt(x-5))

\int \frac{1}{x - 5} d x

2 x - 5 + C

Solution steps

\int \frac{1}{x - 5} d x

Apply u-substitution

: \int 2 d u

= \int 2 d u

Integral of a constant:

\int a d x = a x

= 2 u

Substitute back

u = x - 5

= 2 x - 5

Add a constant to the solution

= 2 x - 5 + C

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\int \frac{1}{( 8 x - 1 ) ^{2}} d x

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What is the integral of 1/(sqrt(x-5)) ?
The integral of 1/(sqrt(x-5)) is 2sqrt(x-5)+C