What is the integral of 1/(sqrt(x)(\sqrt{x)-7)} ?

The integral of 1/(sqrt(x)(\sqrt{x)-7)} is 2ln|sqrt(x)-7|+C

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integral of 1/(sqrt(x)(\sqrt{x)-7)}

\int \frac{1}{x ( x - 7 )} d x

2 ln x - 7 + C

Solution steps

\int \frac{1}{x ( x - 7 )} d x

Apply u-substitution

: \int \frac{2}{u} d u

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = x - 7

= 2 ln x - 7

Add a constant to the solution

= 2 ln x - 7 + C

\frac{d}{d y} (\frac{x ^{2} y ^{2} + 2 x y ^{3}}{( x + y ) ^{2}})

\int x sin (x) d x

\frac{d}{d x} (\frac{2 - sec ( x )}{tan ( x )})

y = 2 - 3 x, x = - 2, x = 2, y = 0

\int_{- 2}^{2} x^{3} d x

What is the integral of 1/(sqrt(x)(\sqrt{x)-7)} ?
The integral of 1/(sqrt(x)(\sqrt{x)-7)} is 2ln|sqrt(x)-7|+C