What is the integral of sqrt(9/4 x+1) ?

The integral of sqrt(9/4 x+1) is 1/27 (9x+4)^{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(9/4 x+1)

\int \frac{9}{4} x + 1 d x

\frac{1}{27} (9 x + 4)^{\frac{3}{2}} + C

Solution steps

\int \frac{9}{4} x + 1 d x

Apply u-substitution

: \int \frac{4 u}{9} d u

= \int \frac{4 u}{9} d u

Take the constant out:

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

= \frac{4}{9} \cdot \int u d u

Apply the Power Rule

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

= \frac{4}{9} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = \frac{9}{4} x + 1

= \frac{4}{9} \cdot \frac{2}{3} (\frac{9}{4} x + 1)^{\frac{3}{2}}

Simplify

\frac{4}{9} \cdot \frac{2}{3} (\frac{9}{4} x + 1)^{\frac{3}{2}} : \frac{1}{27} (9 x + 4)^{\frac{3}{2}}

= \frac{1}{27} (9 x + 4)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{27} (9 x + 4)^{\frac{3}{2}} + C

\int \frac{1}{1 - 2 u} d u

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

\int \frac{27}{x ^{4}} d x

\int sec^{2} (5 x) tan (5 x) d x

\int y 4 y^{2} - 1 d y

What is the integral of sqrt(9/4 x+1) ?
The integral of sqrt(9/4 x+1) is 1/27 (9x+4)^{3/2}+C