What is the integral from-infinity to 3 of 3/(x^2+9) ?

The integral from-infinity to 3 of 3/(x^2+9) is (3pi)/4

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integral from-infinity to 3 of 3/(x^2+9)

\int_{- \infty}^{3} \frac{3}{x ^{2} + 9} d x

\frac{3 π}{4}

Decimal Notation

2.35619 \dots

Solution steps

\int_{- \infty}^{3} \frac{3}{x ^{2} + 9} d x

Compute the indefinite integral:

\int \frac{3}{x ^{2} + 9} d x = arctan (\frac{x}{3}) + C

Compute the boundaries:

\int_{- \infty}^{3} \frac{3}{x ^{2} + 9} d x = \frac{π}{4} - (- \frac{π}{2})

= \frac{π}{4} - (- \frac{π}{2})

Simplify

= \frac{3 π}{4}

f (x) = x + 2, x = 1, x = 3

y^{^{'}} = \frac{x - y}{x + 2 y}

\frac{d ^{2}}{d x ^{2}} (\frac{x}{4 - 6 x})

t^{2} + 2 t + 50

\frac{d}{d x} (t (a + b t))

What is the integral from-infinity to 3 of 3/(x^2+9) ?
The integral from-infinity to 3 of 3/(x^2+9) is (3pi)/4