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

The integral of 1/(4+sqrt(x)) is 2(4+sqrt(x)-4ln|4+sqrt(x)|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(4+sqrt(x))

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

2 (4 + x - 4 ln 4 + x) + C

Solution steps

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

Apply u-substitution

: \int \frac{2 ( u - 4 )}{u} d u

= \int \frac{2 ( u - 4 )}{u} d u

Take the constant out:

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

= 2 \cdot \int \frac{u - 4}{u} d u

Expand

\frac{u - 4}{u} : 1 - \frac{4}{u}

= 2 \cdot \int 1 - \frac{4}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int 1 d u - \int \frac{4}{u} d u)

\int 1 d u = u

\int \frac{4}{u} d u = 4 ln ∣ u ∣

= 2 (u - 4 ln ∣ u ∣)

Substitute back

u = 4 + x

= 2 (4 + x - 4 ln 4 + x)

Add a constant to the solution

= 2 (4 + x - 4 ln 4 + x) + C

\int - 10 x^{2} d x

\int \frac{x ^{3} + x + 1}{x ^{2} + 1} d x

\int 7 x^{- \frac{2}{3}} - 2 x^{\frac{5}{3}} d x

\int \frac{e ^{y}}{( e ^{y} - 2 ) ln ( e ^{y} - 2 )} d y

\int z^{2} e^{z} d z

What is the integral of 1/(4+sqrt(x)) ?
The integral of 1/(4+sqrt(x)) is 2(4+sqrt(x)-4ln|4+sqrt(x)|)+C