What is the integral of sqrt(9x+7) ?

The integral of sqrt(9x+7) is 2/27 (9x+7)^{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(9x+7)

\int 9 x + 7 d x

\frac{2}{27} (9 x + 7)^{\frac{3}{2}} + C

Solution steps

\int 9 x + 7 d x

Apply u-substitution

: \int \frac{u}{9} d u

= \int \frac{u}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{9} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 9 x + 7

= \frac{1}{9} \cdot \frac{2}{3} (9 x + 7)^{\frac{3}{2}}

Simplify

\frac{1}{9} \cdot \frac{2}{3} (9 x + 7)^{\frac{3}{2}} : \frac{2}{27} (9 x + 7)^{\frac{3}{2}}

= \frac{2}{27} (9 x + 7)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{27} (9 x + 7)^{\frac{3}{2}} + C

\int (x^{2} cos (2 x)) d x

\int \frac{3000}{1 + 0.25 x} d x

\int 3 x sin (2 x + 5) d x

\int \frac{1}{2 x + 5} d x

\int \frac{5}{1 - 9 x ^{2}} d x

What is the integral of sqrt(9x+7) ?
The integral of sqrt(9x+7) is 2/27 (9x+7)^{3/2}+C