Precalculus Examples

$x y \log (\frac{x}{y}) d x + (y^{2} - x^{2} \log (\frac{x}{y}) d y)$

Step 1

Remove parentheses.

$x y \log (\frac{x}{y}) d x + y^{2} - x^{2} \log (\frac{x}{y}) d y$

Step 2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

$x \cdot x y \log (\frac{x}{y}) d + y^{2} - x^{2} \log (\frac{x}{y}) d y$

Step 2.2

Multiply $x$ by $x$ .

$x^{2} y \log (\frac{x}{y}) d + y^{2} - x^{2} \log (\frac{x}{y}) d y$

Step 3

Combine the opposite terms in $x^{2} y \log (\frac{x}{y}) d + y^{2} - x^{2} \log (\frac{x}{y}) d y$ .

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Step 3.1

Reorder the factors in the terms $x^{2} y \log (\frac{x}{y}) d$ and $- x^{2} \log (\frac{x}{y}) d y$ .

$x^{2} d y \log (\frac{x}{y}) + y^{2} - x^{2} d y \log (\frac{x}{y})$

Step 3.2

Subtract $x^{2} d y \log (\frac{x}{y})$ from $x^{2} d y \log (\frac{x}{y})$ .

$y^{2} + 0$

Step 3.3

Add $y^{2}$ and $0$ .

$y^{2}$