What is the integral from 1 to infinity of 3/(1+x^2) ?

The integral from 1 to infinity of 3/(1+x^2) is (3pi)/4

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integral from 1 to infinity of 3/(1+x^2)

\int_{1}^{\infty} \frac{3}{1 + x ^{2}} d x

\frac{3 π}{4}

Decimal

2.35619 \dots

Solution steps

\int_{1}^{\infty} \frac{3}{1 + x ^{2}} d x

Compute the indefinite integral:

\int \frac{3}{1 + x ^{2}} d x = 3 arctan (x) + C

Compute the boundaries:

\int_{1}^{\infty} \frac{3}{1 + x ^{2}} d x = 3 \cdot \frac{π}{2} - 3 \cdot \frac{π}{4}

= 3 \cdot \frac{π}{2} - 3 \cdot \frac{π}{4}

Simplify

= \frac{3 π}{4}

\int_{0}^{x} \frac{t}{1 + t ^{2}} d t

\int_{0}^{π} π^{2} - x^{2} d x

\int_{0}^{1} x - 2 d x

\int_{1}^{e^{4}} x ln (x) d x

\int_{2}^{4} 9 x^{2} d x

What is the integral from 1 to infinity of 3/(1+x^2) ?
The integral from 1 to infinity of 3/(1+x^2) is (3pi)/4