What is the integral of x/(x^4+10) ?

The integral of x/(x^4+10) is 1/(2sqrt(10))arctan((x^2)/(sqrt(10)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/(x^4+10)

\int \frac{x}{x ^{4} + 10} d x

\frac{1}{2 10} arctan (\frac{x ^{2}}{10}) + C

Solution steps

\int \frac{x}{x ^{4} + 10} d x

Apply u-substitution

: \int \frac{1}{2 ( u ^{2} + 10 )} d u

= \int \frac{1}{2 ( u ^{2} + 10 )} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u ^{2} + 10} d u

Apply Integral Substitution

= \frac{1}{2} \cdot \int \frac{1}{10 ( v ^{2} + 1 )} d v

Take the constant out:

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

= \frac{1}{2} \cdot \frac{1}{10} \cdot \int \frac{1}{v ^{2} + 1} d v

Use the common integral:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= \frac{1}{2} \cdot \frac{1}{10} arctan (v)

Substitute back

= \frac{1}{2} \cdot \frac{1}{10} arctan (\frac{x ^{2}}{10})

Simplify

\frac{1}{2} \cdot \frac{1}{10} arctan (\frac{x ^{2}}{10}) : \frac{1}{2 10} arctan (\frac{x ^{2}}{10})

= \frac{1}{2 10} arctan (\frac{x ^{2}}{10})

Add a constant to the solution

= \frac{1}{2 10} arctan (\frac{x ^{2}}{10}) + C

\frac{x}{x - 1}

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

lo g_{10} ((arcsin (x))^{2})

(- x^{3} + 4 x^{2} - 5 x)^{^{'}}

(x, y) \to (π, \frac{π}{2}) lim (y sin (x - y))

What is the integral of x/(x^4+10) ?
The integral of x/(x^4+10) is 1/(2sqrt(10))arctan((x^2)/(sqrt(10)))+C