What is the integral of (xy)/(1+x^4) ?

The integral of (xy)/(1+x^4) is x/(1+x^4)*(y^2)/2+C

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integral of (xy)/(1+x^4)

\int \frac{x y}{1 + x ^{4}} d y

\frac{x}{1 + x ^{4}} \cdot \frac{y ^{2}}{2} + C

Solution steps

\int \frac{x y}{1 + x ^{4}} d y

Take the constant out:

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

= \frac{x}{1 + x ^{4}} \cdot \int y d y

Apply the Power Rule

: \frac{y ^{2}}{2}

= \frac{x}{1 + x ^{4}} \cdot \frac{y ^{2}}{2}

Add a constant to the solution

= \frac{x}{1 + x ^{4}} \cdot \frac{y ^{2}}{2} + C

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What is the integral of (xy)/(1+x^4) ?
The integral of (xy)/(1+x^4) is x/(1+x^4)*(y^2)/2+C