What is the integral from 1 to infinity of 7/(1+x^2) ?

The integral from 1 to infinity of 7/(1+x^2) is (7pi)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to infinity of 7/(1+x^2)

\int_{1}^{\infty} \frac{7}{1 + x ^{2}} d x

\frac{7 π}{4}

Decimal

5.49778 \dots

Solution steps

\int_{1}^{\infty} \frac{7}{1 + x ^{2}} d x

Compute the indefinite integral:

\int \frac{7}{1 + x ^{2}} d x = 7 arctan (x) + C

Compute the boundaries:

\int_{1}^{\infty} \frac{7}{1 + x ^{2}} d x = 7 \cdot \frac{π}{2} - 7 \cdot \frac{π}{4}

= 7 \cdot \frac{π}{2} - 7 \cdot \frac{π}{4}

Simplify

= \frac{7 π}{4}

What is the integral from 1 to infinity of 7/(1+x^2) ?
The integral from 1 to infinity of 7/(1+x^2) is (7pi)/4