What is the integral of sqrt(-4x) ?

The integral of sqrt(-4x) is i 1/3 (-2x^{3/2}+6xsqrt(x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(-4x)

\int - 4 x d x

i \frac{1}{3} (- 2 x^{\frac{3}{2}} + 6 x x) + C

Solution steps

\int - 4 x d x

- 4 x = 4 - x

= \int 4 - x d x

Take the constant out:

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

= 4 \cdot \int - x d x

4 = 2

= 2 \cdot \int - x d x

Apply Integration By Parts

: x - x - \int - \frac{x}{2 - x} d x

= 2 (x - x - \int - \frac{x}{2 - x} d x)

\int - \frac{x}{2 - x} d x = \frac{i x ^{\frac{3}{2}}}{3}

= 2 (x - x - \frac{i x ^{\frac{3}{2}}}{3})

Simplify

2 (x - x - \frac{i x ^{\frac{3}{2}}}{3}) : i \frac{1}{3} (- 2 x^{\frac{3}{2}} + 6 x x)

= i \frac{1}{3} (- 2 x^{\frac{3}{2}} + 6 x x)

Add a constant to the solution

= i \frac{1}{3} (- 2 x^{\frac{3}{2}} + 6 x x) + C

\int (2 x + 8) sin (2 x) d x

\int \frac{x}{cos ^{2} ( 2 x )} d x

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

\int \frac{x}{a + 2 x} d x

\int 4^{x + \frac{1}{2}} d x

What is the integral of sqrt(-4x) ?
The integral of sqrt(-4x) is i 1/3 (-2x^{3/2}+6xsqrt(x))+C