What is the integral of 5/(sqrt(x-7)) ?

The integral of 5/(sqrt(x-7)) is 10sqrt(x-7)+C

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integral of 5/(sqrt(x-7))

\int \frac{5}{x - 7} d x

10 x - 7 + C

Solution steps

\int \frac{5}{x - 7} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{x - 7} d x

Apply u-substitution

: \int 2 d u

= 5 \cdot \int 2 d u

Integral of a constant:

\int a d x = a x

= 5 \cdot 2 u

Substitute back

u = x - 7

= 5 \cdot 2 x - 7

Simplify

= 10 x - 7

Add a constant to the solution

= 10 x - 7 + C

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What is the integral of 5/(sqrt(x-7)) ?
The integral of 5/(sqrt(x-7)) is 10sqrt(x-7)+C