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

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

\int \frac{( x + 7 ) ^{6}}{2 x} d x

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

Solution steps

\int \frac{( x + 7 ) ^{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 + 7 ) ^{6}}{x} d x

Apply u-substitution

: \int 2 u^{6} d u

= \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{u ^{7}}{7}

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

Substitute back

u = x + 7

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

Simplify

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

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

Add a constant to the solution

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

\int cos (\frac{π}{2} - x) d x

\int \frac{2 - x}{9 x ^{4} + x ^{2}} d x

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

\int sin (wt) e^{- s t} d t

\int (x^{2} - 6)^{2} d x

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