What is the integral from 1 to infinity of 5/(1+x^2) ?

The integral from 1 to infinity of 5/(1+x^2) is (5pi)/4

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integral from 1 to infinity of 5/(1+x^2)

\int_{1}^{\infty} \frac{5}{1 + x ^{2}} d x

\frac{5 π}{4}

Decimal

3.92699 \dots

Solution steps

\int_{1}^{\infty} \frac{5}{1 + x ^{2}} d x

Compute the indefinite integral:

\int \frac{5}{1 + x ^{2}} d x = 5 arctan (x) + C

Compute the boundaries:

\int_{1}^{\infty} \frac{5}{1 + x ^{2}} d x = 5 \cdot \frac{π}{2} - 5 \cdot \frac{π}{4}

= 5 \cdot \frac{π}{2} - 5 \cdot \frac{π}{4}

Simplify

= \frac{5 π}{4}

What is the integral from 1 to infinity of 5/(1+x^2) ?
The integral from 1 to infinity of 5/(1+x^2) is (5pi)/4