Calculus Examples

$\frac{d y}{d x} = \frac{u x - x}{u x - x}$

Step 1

Rewrite the equation.

$d y = \frac{u x - x}{u x - x} d x$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d y = \int \frac{u x - x}{u x - x} d x$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int \frac{u x - x}{u x - x} d x$

Step 2.3

Integrate the right side.

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Step 2.3.1

Cancel the common factor of $u x - x$ .

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Step 2.3.1.1

Cancel the common factor.

$y + C_{1} = \int \frac{u x - x}{u x - x} d x$

Step 2.3.1.2

Rewrite the expression.

$y + C_{1} = \int d x$

Step 2.3.2

Apply the constant rule.

$y + C_{1} = x + C_{2}$

Step 2.4

Group the constant of integration on the right side as $K$ .

$y = x + K$