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

The integral of sqrt(4x+3) is 1/6 (4x+3)^{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(4x+3)

\int 4 x + 3 d x

\frac{1}{6} (4 x + 3)^{\frac{3}{2}} + C

Solution steps

\int 4 x + 3 d x

Apply u-substitution

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

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

Take the constant out:

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

= \frac{1}{4} \cdot \int u d u

Apply the Power Rule

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

= \frac{1}{4} \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 4 x + 3

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

Simplify

\frac{1}{4} \cdot \frac{2}{3} (4 x + 3)^{\frac{3}{2}} : \frac{1}{6} (4 x + 3)^{\frac{3}{2}}

= \frac{1}{6} (4 x + 3)^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{6} (4 x + 3)^{\frac{3}{2}} + C

2 x y d y = (y^{2} + 1) d x

\frac{d}{d x} (\frac{3 x}{7})

\int e^{2 x} (1 - 7 e^{2 x})^{2} d x

\int \frac{175}{e ^{- x} + 1} d x

\frac{d}{d x} (ln (7) x^{2})

What is the integral of sqrt(4x+3) ?
The integral of sqrt(4x+3) is 1/6 (4x+3)^{3/2}+C