What is the integral of 3*sqrt(x+4) ?

The integral of 3*sqrt(x+4) is 2(x+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 3*sqrt(x+4)

\int 3 \cdot x + 4 d x

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

Solution steps

\int 3 x + 4 d x

Take the constant out:

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

= 3 \cdot \int x + 4 d x

Apply u-substitution

: \int u d u

= 3 \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = x + 4

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

Simplify

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

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

Add a constant to the solution

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

n = 0 \sum \infty \frac{4}{n ^{2}}

\frac{d y}{d x} 9 x^{2} y + 9 y^{2} x = - 9

\int e^{2 x - 2} d x

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

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

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