What is the integral of ((sqrt(x)+7)^3)/(2sqrt(x)) ?

The integral of ((sqrt(x)+7)^3)/(2sqrt(x)) is 1/4 (sqrt(x)+7)^4+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)+7)^3)/(2sqrt(x))

\int \frac{( x + 7 ) ^{3}}{2 x} d x

\frac{1}{4} (x + 7)^{4} + C

Solution steps

\int \frac{( x + 7 ) ^{3}}{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 + 7 ) ^{3}}{x} d x

Apply u-substitution

: \int 2 u^{3} d u

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

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{1}{2} \cdot 2 \cdot \frac{u ^{4}}{4}

Substitute back

u = x + 7

= \frac{1}{2} \cdot 2 \cdot \frac{( x + 7 ) ^{4}}{4}

Simplify

\frac{1}{2} \cdot 2 \cdot \frac{( x + 7 ) ^{4}}{4} : \frac{1}{4} (x + 7)^{4}

= \frac{1}{4} (x + 7)^{4}

Add a constant to the solution

= \frac{1}{4} (x + 7)^{4} + C

\frac{d P}{d t} = 2 Pt, P (1) = 7

\int 5 x^{2} d x

\frac{\partial}{\partial x} (\frac{x}{1 - x ^{2} y ^{2}})

y = x^{2} + 4

f (x^{3} - x)

What is the integral of ((sqrt(x)+7)^3)/(2sqrt(x)) ?
The integral of ((sqrt(x)+7)^3)/(2sqrt(x)) is 1/4 (sqrt(x)+7)^4+C