What is the integral from-infinity to infinity of (2x)/((x^2+1)^{12)} ?

The integral from-infinity to infinity of (2x)/((x^2+1)^{12)} is 0

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integral from-infinity to infinity of (2x)/((x^2+1)^{12)}

\int_{- \infty}^{\infty} \frac{2 x}{( x ^{2} + 1 ) ^{12}} d x

0

Solution steps

\int_{- \infty}^{\infty} \frac{2 x}{( x ^{2} + 1 ) ^{12}} d x

Compute the indefinite integral:

\int \frac{2 x}{( x ^{2} + 1 ) ^{12}} d x = - \frac{1}{11 ( x ^{2} + 1 ) ^{11}} + C

Compute the boundaries:

\int_{- \infty}^{\infty} \frac{2 x}{( x ^{2} + 1 ) ^{12}} d x = 0 - 0

= 0 - 0

Simplify

= 0

\frac{d y}{d x} = y (2 x - 5)

x \to 4 lim (\frac{x ^{2} - 8 x + 16}{x - 4})

cos (5 x)

\frac{d}{d x} (\frac{x}{e ^{x}})

y^{^{'}} + 2 y = 6 e^{x}

What is the integral from-infinity to infinity of (2x)/((x^2+1)^{12)} ?
The integral from-infinity to infinity of (2x)/((x^2+1)^{12)} is 0