Calculus Examples

$\frac{d y}{d x} = \frac{0}{1 + 1}$

Step 1

Rewrite the equation.

$d y = \frac{0}{1 + 1} d x$

Step 2

Integrate both sides.

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Step 2.1

Set up an integral on each side.

$\int d y = \int \frac{0}{1 + 1} d x$

Step 2.2

Apply the constant rule.

$y + C_{1} = \int \frac{0}{1 + 1} d x$

Step 2.3

Integrate the right side.

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Step 2.3.1

Simplify.

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Step 2.3.1.1

Add $1$ and $1$ .

$y + C_{1} = \int \frac{0}{2} d x$

Step 2.3.1.2

Cancel the common factor of $0$ and $2$ .

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Step 2.3.1.2.1

Factor $2$ out of $0$ .

$y + C_{1} = \int \frac{2 (0)}{2} d x$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $2$ .

$y + C_{1} = \int \frac{2 \cdot 0}{2 \cdot 1} d x$

Step 2.3.1.2.2.2

Cancel the common factor.

$y + C_{1} = \int \frac{2 \cdot 0}{2 \cdot 1} d x$

Step 2.3.1.2.2.3

Rewrite the expression.

$y + C_{1} = \int \frac{0}{1} d x$

Step 2.3.1.2.2.4

Divide $0$ by $1$ .

$y + C_{1} = \int 0 d x$

Step 2.3.2

The integral of $0$ with respect to $x$ is $0$ .

$y + C_{1} = 0 + C_{2}$

Step 2.3.3

Add $0$ and $C_{2}$ .

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

Step 2.4

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

$y = D$