What is the integral from 0 to 2 of x/((1+x^2)^4) ?

The integral from 0 to 2 of x/((1+x^2)^4) is 62/375

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 2 of x/((1+x^2)^4)

\int_{0}^{2} \frac{x}{( 1 + x ^{2} ) ^{4}} d x

\frac{62}{375}

Decimal

0.16533 \dots

Solution steps

\int_{0}^{2} \frac{x}{( 1 + x ^{2} ) ^{4}} d x

Apply u-substitution

= \int_{1}^{5} \frac{1}{2 u ^{4}} 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_{1}^{5} \frac{1}{u ^{4}} d u

Apply the Power Rule

= \frac{1}{2} [- \frac{1}{3 u ^{3}}]_{1}^{5}

Compute the boundaries:

\frac{124}{375}

= \frac{1}{2} \cdot \frac{124}{375}

Simplify

= \frac{62}{375}

What is the integral from 0 to 2 of x/((1+x^2)^4) ?
The integral from 0 to 2 of x/((1+x^2)^4) is 62/375