Constant Rule Integration Calculator

Published on: July 17, 2026
Final Answer: Free • Full Steps: Plus

This Constant Rule Integration Calculator integrates a plain number, and shows the working line by line. A constant integrates to that constant multiplied by x, because a straight line with that slope is the function whose derivative is the constant. The constant of integration is then added at the end, since any number would have vanished on differentiating. Following the same pattern every time keeps the x from being left off the answer.

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule for integration.
  3. Multiply the constant by x and add the constant of integration C.

Formula:

\(\int k\, dx = kx + C\)
See Example 1 Hide Example 1

Problem

\(\int 7\, dx\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule for integration.
  3. Multiply the constant by x and add the constant of integration C.

Step 1

Step 1 - Identify the constant k.

In this problem: The constant is \(k = 7\).

\(\int 7\, dx\)

Step 2

Step 2 - Write the constant rule for integration.

In this problem: The integral of a constant is the constant times x.

\(\int k\, dx = kx + C\)

Step 3

Step 3 - Multiply the constant by x and add the constant of integration C.

In this problem: The antiderivative is \(7 x\).

\(\int 7\, dx = 7 x + C\)

Final Answer

\(\int 7\, dx = 7 x + C\)
See Example 2 Hide Example 2

Problem

\(\int -3\, dx\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule for integration.
  3. Multiply the constant by x and add the constant of integration C.

Step 1

Step 1 - Identify the constant k.

In this problem: The constant is \(k = -3\).

\(\int -3\, dx\)

Step 2

Step 2 - Write the constant rule for integration.

In this problem: The integral of a constant is the constant times x.

\(\int k\, dx = kx + C\)

Step 3

Step 3 - Multiply the constant by x and add the constant of integration C.

In this problem: The antiderivative is \(- 3 x\).

\(\int -3\, dx = - 3 x + C\)

Final Answer

\(\int -3\, dx = - 3 x + C\)

Example Problems

Click one to load it into the box and solve it.