# Calculus Examples

Step 1

Rewrite the equation.

Step 2

Step 2.1

Set up an integral on each side.

Step 2.2

Apply the constant rule.

Step 2.3

Integrate the right side.

Step 2.3.1

Let . Then . Rewrite using and .

Step 2.3.1.1

Let . Find .

Step 2.3.1.1.1

Differentiate .

Step 2.3.1.1.2

By the Sum Rule, the derivative of with respect to is .

Step 2.3.1.1.3

Differentiate using the Power Rule which states that is where .

Step 2.3.1.1.4

Since is constant with respect to , the derivative of with respect to is .

Step 2.3.1.1.5

Add and .

Step 2.3.1.2

Rewrite the problem using and .

Step 2.3.2

By the Power Rule, the integral of with respect to is .

Step 2.3.3

Replace all occurrences of with .

Step 2.4

Group the constant of integration on the right side as .