What is the integral of 1/(2sqrt(x)+2x) ?

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

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

ln 1 + x + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{1 + u} d u

= \int \frac{1}{1 + u} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln 1 + x

Add a constant to the solution

= ln 1 + x + C

\frac{3}{( 8 z + 16 )}

\frac{d}{d x} (\frac{2}{( x + 1 ) ( - x + 1 )})

t \to 1 lim (cos (t π))

f (x) = \frac{2}{x ^{3}}

y = \frac{12}{1 + x ^{4}}, y = 6 x^{2}

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