What is the integral of 1/(-10sqrt(x)-10x) ?

The integral of 1/(-10sqrt(x)-10x) is -1/5 ln|sqrt(x)+1|+C

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integral of 1/(-10sqrt(x)-10x)

\int \frac{1}{- 10 x - 10 x} d x

- \frac{1}{5} ln x + 1 + C

Solution steps

\int \frac{1}{- 10 x - 10 x} d x

Apply u-substitution

: \int - \frac{1}{5 ( u + 1 )} d u

= \int - \frac{1}{5 ( u + 1 )} d u

Take the constant out:

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

= - \frac{1}{5} \cdot \int \frac{1}{u + 1} d u

Apply u-substitution

: \int \frac{1}{v} d v

= - \frac{1}{5} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= - \frac{1}{5} ln ∣ v ∣

Substitute back

= - \frac{1}{5} ln x + 1

Add a constant to the solution

= - \frac{1}{5} ln x + 1 + C

\int \frac{8}{x ( x ^{2} + 25 )} d x

\frac{d}{d x} (x^{2} arcsin (x))

x \to 0 lim (\frac{y}{x})

\frac{d y}{d x}, e^{\frac{x}{y}} = 7 x - y

x y^{^{'}} - 2 y = x

What is the integral of 1/(-10sqrt(x)-10x) ?
The integral of 1/(-10sqrt(x)-10x) is -1/5 ln|sqrt(x)+1|+C