What is the integral of ((sqrt(x)+8)^6)/(2sqrt(x)) ?

The integral of ((sqrt(x)+8)^6)/(2sqrt(x)) is 1/7 (sqrt(x)+8)^7+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ((sqrt(x)+8)^6)/(2sqrt(x))

\int \frac{( x + 8 ) ^{6}}{2 x} d x

\frac{1}{7} (x + 8)^{7} + C

Solution steps

\int \frac{( x + 8 ) ^{6}}{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 + 8 ) ^{6}}{x} d x

Apply u-substitution

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

Apply the Power Rule

= \frac{1}{2} \cdot 2 \cdot \frac{u ^{7}}{7}

Substitute back

u = x + 8

= \frac{1}{2} \cdot 2 \cdot \frac{( x + 8 ) ^{7}}{7}

Simplify

\frac{1}{2} \cdot 2 \cdot \frac{( x + 8 ) ^{7}}{7} : \frac{1}{7} (x + 8)^{7}

= \frac{1}{7} (x + 8)^{7}

Add a constant to the solution

= \frac{1}{7} (x + 8)^{7} + C

What is the integral of ((sqrt(x)+8)^6)/(2sqrt(x)) ?
The integral of ((sqrt(x)+8)^6)/(2sqrt(x)) is 1/7 (sqrt(x)+8)^7+C