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

The integral of ((sqrt(x)+3)^4)/(2sqrt(x)) is 1/5 (sqrt(x)+3)^5+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)+3)^4)/(2sqrt(x))

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

\frac{1}{5} (x + 3)^{5} + C

Solution steps

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

Apply u-substitution

: \int 2 u^{4} d u

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

Apply the Power Rule

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

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

Substitute back

u = x + 3

= \frac{1}{2} \cdot 2 \cdot \frac{( x + 3 ) ^{5}}{5}

Simplify

\frac{1}{2} \cdot 2 \cdot \frac{( x + 3 ) ^{5}}{5} : \frac{1}{5} (x + 3)^{5}

= \frac{1}{5} (x + 3)^{5}

Add a constant to the solution

= \frac{1}{5} (x + 3)^{5} + C

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

\int (ln (1 + x)) d x

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

\int c e^{- \frac{x}{2}} d x

What is the integral of ((sqrt(x)+3)^4)/(2sqrt(x)) ?
The integral of ((sqrt(x)+3)^4)/(2sqrt(x)) is 1/5 (sqrt(x)+3)^5+C