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

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

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integral of 1/(sqrt(-x))

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

- 2 i x + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - 2 u^{\frac{1}{2}}

Substitute back

u = - x

= - 2 (- x)^{\frac{1}{2}}

(- x)^{\frac{1}{2}} = i x

= - 2 i x

Add a constant to the solution

= - 2 i x + C

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