What is the integral of (5(4+sqrt(x)))/(sqrt(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5(4+sqrt(x)))/(sqrt(x))

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

5 (4 + x)^{2} + C

Solution steps

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

Take the constant out:

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

= 5 \cdot \int \frac{4 + x}{x} d x

Apply u-substitution

: \int 2 u d u

= 5 \cdot \int 2 u d u

Take the constant out:

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

= 5 \cdot 2 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

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

Substitute back

u = 4 + x

= 5 \cdot 2 \cdot \frac{( 4 + x ) ^{2}}{2}

Simplify

5 \cdot 2 \cdot \frac{( 4 + x ) ^{2}}{2} : 5 (4 + x)^{2}

= 5 (4 + x)^{2}

Add a constant to the solution

= 5 (4 + x)^{2} + C

\int (\frac{1}{x ^{2}}) sin (\frac{π}{x}) d x

\int t^{2} sin (θ) t d t

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

\int cos (x) \cdot cos (sin (x)) d x

\int 20 x sin (7 x^{2} - 8) d x

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