What is the integral of sqrt(15x-2) ?

The integral of sqrt(15x-2) is 2/45 (15x-2)^{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(15x-2)

\int 15 x - 2 d x

\frac{2}{45} (15 x - 2)^{\frac{3}{2}} + C

Solution steps

\int 15 x - 2 d x

Apply u-substitution

: \int \frac{u}{15} d u

= \int \frac{u}{15} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{15} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 15 x - 2

= \frac{1}{15} \cdot \frac{2}{3} (15 x - 2)^{\frac{3}{2}}

Simplify

\frac{1}{15} \cdot \frac{2}{3} (15 x - 2)^{\frac{3}{2}} : \frac{2}{45} (15 x - 2)^{\frac{3}{2}}

= \frac{2}{45} (15 x - 2)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{45} (15 x - 2)^{\frac{3}{2}} + C

\int \frac{1}{\frac{1 - x ^{2}}{100}} d x

\int x (4 - 10 e^{- 0.2 x}) d x

\int (e^{x} + \frac{3}{x} + sin (x)) d x

\int 4 (4 x + 2) d x

\int - \frac{15}{x ^{16}} d x

What is the integral of sqrt(15x-2) ?
The integral of sqrt(15x-2) is 2/45 (15x-2)^{3/2}+C