What is the integral of (xy^2)/(x^2+1) ?

The integral of (xy^2)/(x^2+1) is x/(1+x^2)*(y^3)/3+C

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integral of (xy^2)/(x^2+1)

\int \frac{x y ^{2}}{x ^{2} + 1} d y

\frac{x}{1 + x ^{2}} \cdot \frac{y ^{3}}{3} + C

Solution steps

\int \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 y^{2} d y

Apply the Power Rule

: \frac{y ^{3}}{3}

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

Add a constant to the solution

= \frac{x}{1 + x ^{2}} \cdot \frac{y ^{3}}{3} + C

x \to - \infty lim (tanh (x))

\int sec (t) tan (t) d t

g (x) = x^{2} (1 - 4 x)

\frac{d}{d x} (e^{x} (1 - x^{2}))

f (x) = \frac{8}{x}

What is the integral of (xy^2)/(x^2+1) ?
The integral of (xy^2)/(x^2+1) is x/(1+x^2)*(y^3)/3+C