What is the integral of x/(sqrt(2x+5)) ?

The integral of x/(sqrt(2x+5)) is 1/3 (x-5)sqrt(2x+5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/(sqrt(2x+5))

\int \frac{x}{2 x + 5} d x

\frac{1}{3} (x - 5) 2 x + 5 + C

Solution steps

\int \frac{x}{2 x + 5} d x

Apply u-substitution

: \int \frac{u ^{2} - 5}{2} d u

= \int \frac{u ^{2} - 5}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{2} - 5 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int u^{2} d u - \int 5 d u)

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

\int 5 d u = 5 u

= \frac{1}{2} (\frac{u ^{3}}{3} - 5 u)

Substitute back

u = 2 x + 5

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

Simplify

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

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

Add a constant to the solution

= \frac{1}{3} (x - 5) 2 x + 5 + C

\int_{0}^{2} x \cdot e^{- x} d x

x \to 0 + lim (\frac{1}{sin ( x )})

\frac{d}{d x} ((x^{2} + 7) (5 - x))

\int 3 - x^{2} d x

\frac{\partial}{\partial y} (3 y^{2} x + x^{3} + y x^{2})

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