What is the integral of (2x-3)^{1/2} ?

The integral of (2x-3)^{1/2} is 1/3 (2x-3)^{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 (2x-3)^{1/2}

\int (2 x - 3)^{\frac{1}{2}} d x

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

Solution steps

\int (2 x - 3)^{\frac{1}{2}} d x

Apply u-substitution

: \int \frac{u ^{\frac{1}{2}}}{2} d u

= \int \frac{u ^{\frac{1}{2}}}{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^{\frac{1}{2}} 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 = 2 x - 3

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{1}{2} e^{- 4 x} + sin (x) d x

\int \frac{2 e ^{x}}{3 + e ^{x}} d x

\int (- 9 + \frac{8}{x}) d x

\int \frac{18}{x ( x ^{2} - 9 )} d x

\int (18 x + 8) d x

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