What is the integral of 1/(3sqrt(x)(5+\sqrt{x))} ?

The integral of 1/(3sqrt(x)(5+\sqrt{x))} is 2/3 ln|5+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/(3sqrt(x)(5+\sqrt{x))}

\int \frac{1}{3 x ( 5 + x )} d x

\frac{2}{3} ln 5 + x + C

Solution steps

\int \frac{1}{3 x ( 5 + x )} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int \frac{1}{x ( 5 + x )} d x

Apply u-substitution

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

= \frac{1}{3} \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}{3} \cdot 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} \cdot 2 ln ∣ u ∣

Substitute back

u = 5 + x

= \frac{1}{3} \cdot 2 ln 5 + x

Simplify

\frac{1}{3} \cdot 2 ln 5 + x : \frac{2}{3} ln 5 + x

= \frac{2}{3} ln 5 + x

Add a constant to the solution

= \frac{2}{3} ln 5 + x + C

y = x^{4} + 7 e^{x}, (0, 7)

x \to 2 - lim (H (x))

\frac{d}{d x} (x (2 x + 9)^{\frac{1}{3}})

\int_{0}^{\infty} t e^{- k t} d t

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

What is the integral of 1/(3sqrt(x)(5+\sqrt{x))} ?
The integral of 1/(3sqrt(x)(5+\sqrt{x))} is 2/3 ln|5+sqrt(x)|+C