What is the integral of sqrt((2x+21)) ?

The integral of sqrt((2x+21)) is 1/3 (2x+21)^{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((2x+21))

\int (2 x + 21) d x

\frac{1}{3} (2 x + 21)^{\frac{3}{2}} + C

Solution steps

\int 2 x + 21 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 = 2 x + 21

= \frac{1}{2} \cdot \frac{2}{3} (2 x + 21)^{\frac{3}{2}}

Simplify

\frac{1}{2} \cdot \frac{2}{3} (2 x + 21)^{\frac{3}{2}} : \frac{1}{3} (2 x + 21)^{\frac{3}{2}}

= \frac{1}{3} (2 x + 21)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} (2 x + 21)^{\frac{3}{2}} + C

\int \frac{x ^{2}}{2} - x^{4} + 602.5 d x

\int (2 - x cos (x)) d x

\int x^{3} - 2 x^{2} - 5 x + 6 d x

\int cos (x) co x y - cot (x)

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

What is the integral of sqrt((2x+21)) ?
The integral of sqrt((2x+21)) is 1/3 (2x+21)^{3/2}+C