What is the integral of 1/(4sqrt(x)(3+\sqrt{x))} ?

The integral of 1/(4sqrt(x)(3+\sqrt{x))} is 1/2 ln|3+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/(4sqrt(x)(3+\sqrt{x))}

\int \frac{1}{4 x ( 3 + x )} d x

\frac{1}{2} ln 3 + x + C

Solution steps

\int \frac{1}{4 x ( 3 + x )} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{1}{x ( 3 + x )} d x

Apply u-substitution

: \int \frac{2}{u} d u

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{4} \cdot 2 ln ∣ u ∣

Substitute back

u = 3 + x

= \frac{1}{4} \cdot 2 ln 3 + x

Simplify

\frac{1}{4} \cdot 2 ln 3 + x : \frac{1}{2} ln 3 + x

= \frac{1}{2} ln 3 + x

Add a constant to the solution

= \frac{1}{2} ln 3 + x + C

\int \frac{7 x}{x - 1} d x

2 x - x^{2}

x \to \infty lim (\frac{2 x ^{3} + 3 x - 4}{5 - 4 x ^{3}})

f^{^{'}} (x) = x^{2} e^{x}

\frac{d}{d x} (\frac{6 x ^{\frac{3}{2}}}{x})

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