What is the integral of ((2y^{1/2})/(y^3))0x ?

The integral of ((2y^{1/2})/(y^3))0x is -(4x)/(3y^{3/2)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ((2y^{1/2})/(y^3))0x

\int (\frac{2 y ^{\frac{1}{2}}}{y ^{3}}) d^{0} x

- \frac{4 x}{3 y ^{\frac{3}{2}}} + C

Solution steps

\int \frac{2 y ^{\frac{1}{2}}}{y ^{3}} d^{0} x d y

Take the constant out:

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

= 2 d^{0} x \cdot \int \frac{y ^{\frac{1}{2}}}{y ^{3}} d y

Simplify

= 2 x \cdot \int \frac{y ^{\frac{1}{2}}}{y ^{3}} d y

Simplify

\frac{y ^{\frac{1}{2}}}{y ^{3}} : \frac{1}{y ^{\frac{5}{2}}}

= 2 x \cdot \int \frac{1}{y ^{\frac{5}{2}}} d y

Apply the Power Rule

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

Simplify

2 x (- \frac{2}{3 y ^{\frac{3}{2}}}) : - \frac{4 x}{3 y ^{\frac{3}{2}}}

= - \frac{4 x}{3 y ^{\frac{3}{2}}}

Add a constant to the solution

= - \frac{4 x}{3 y ^{\frac{3}{2}}} + C

What is the integral of ((2y^{1/2})/(y^3))0x ?
The integral of ((2y^{1/2})/(y^3))0x is -(4x)/(3y^{3/2)}+C