What is the integral of ((sqrt(x)+2)^5)/(2sqrt(x)) ?

The integral of ((sqrt(x)+2)^5)/(2sqrt(x)) is 1/6 (sqrt(x)+2)^6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((sqrt(x)+2)^5)/(2sqrt(x))

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

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

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{( x + 2 ) ^{5}}{x} d x

Apply u-substitution

: \int 2 u^{5} d u

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{1}{2} \cdot 2 \cdot \frac{u ^{6}}{6}

Substitute back

u = x + 2

= \frac{1}{2} \cdot 2 \cdot \frac{( x + 2 ) ^{6}}{6}

Simplify

\frac{1}{2} \cdot 2 \cdot \frac{( x + 2 ) ^{6}}{6} : \frac{1}{6} (x + 2)^{6}

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

Add a constant to the solution

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

\int \frac{- x ^{2} + 5 x - 4}{( 2 - x ) ^{3}} d x

\int (8 x - a)^{3} d x

\int (2 - 5 x)^{7} d x

\int sin (x) - cos (2 x) d x

\int \frac{3 ( x + 4 )}{x ^{5}} d x

What is the integral of ((sqrt(x)+2)^5)/(2sqrt(x)) ?
The integral of ((sqrt(x)+2)^5)/(2sqrt(x)) is 1/6 (sqrt(x)+2)^6+C