What is the integral of sqrt(1+2x) ?

The integral of sqrt(1+2x) is 1/3 (1+2x)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(1+2x)

\int 1 + 2 x d x

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

Solution steps

\int 1 + 2 x d x

Apply u-substitution

: \int \frac{u}{2} d u

= \int \frac{u}{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 d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{1}{2} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 1 + 2 x

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

Simplify

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

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

Add a constant to the solution

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

ln (144 sin^{2} (x))

\int x^{2} + 2 d x

\frac{d}{d x} ((A x + B) e^{- 2 x})

\int \frac{- 5 x - 3}{x ^{2} + 3 x + 4} d x

\frac{\partial}{\partial x} (x e^{w})

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