en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5u^{3/2}

Solution

\int 5 u^{\frac{3}{2}} d u

Solution

2 u^{\frac{5}{2}} + C

Solution steps

\int 5 u^{\frac{3}{2}} d u

Take the constant out:

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

= 5 \cdot \int u^{\frac{3}{2}} d u

Apply the Power Rule

: \frac{2}{5} u^{\frac{5}{2}}

= 5 \cdot \frac{2}{5} u^{\frac{5}{2}}

Simplify

5 \cdot \frac{2}{5} u^{\frac{5}{2}} : 2 u^{\frac{5}{2}}

= 2 u^{\frac{5}{2}}

Add a constant to the solution

= 2 u^{\frac{5}{2}} + C

Graph

Popular Examples

derivative of (2x-6/(4-x))

\frac{d}{d x} (\frac{2 x - 6}{4 - x})

integral of (x^2)/((x^3+1)^2)

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

derivative of 9/(sqrt(x+4))

\frac{d}{d x} (\frac{9}{x + 4})

derivative of (2x+5/(7x^2))

\frac{d}{d x} (\frac{2 x + 5}{7 x ^{2}})

derivative of log_{6}(cot(8x))

\frac{d}{d x} (lo g_{6} (cot (8 x)))

Frequently Asked Questions (FAQ)

What is the integral of 5u^{3/2} ?
The integral of 5u^{3/2} is 2u^{5/2}+C