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

The integral from-3 to 3 of ((xy^2)/(x^2+1)) is (18x)/(1+x^2)

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

\int_{- 3}^{3} (\frac{x y ^{2}}{x ^{2} + 1}) d y

\frac{18 x}{1 + x ^{2}}

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{x}{1 + x ^{2}} \cdot \int_{- 3}^{3} y^{2} d y

Apply the Power Rule

: [\frac{y ^{3}}{3}]_{- 3}^{3}

= \frac{x}{1 + x ^{2}} [\frac{y ^{3}}{3}]_{- 3}^{3}

Compute the boundaries:

18

= \frac{x}{1 + x ^{2}} \cdot 18

Simplify

= \frac{18 x}{1 + x ^{2}}

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What is the integral from-3 to 3 of ((xy^2)/(x^2+1)) ?
The integral from-3 to 3 of ((xy^2)/(x^2+1)) is (18x)/(1+x^2)