Simplifying Integration of ∫ bˣ dx using Power Rule: Step-by-Step Guide

∫ bˣ dx

To integrate ∫ bˣ dx, where b is a constant, we can follow the following steps:

Step 1: Write down the integral
∫ bˣ dx

Step 2: Simplify the integral
Since b is a constant, we can treat it as such during integration, so the integral becomes:
∫ bˣ dx = b ∫ 1ˣ dx

Step 3: Integrate the function
Using the power rule of integration, where the integral of x^n is (1/(n+1))x^(n+1), we can integrate ∫ 1ˣ dx as follows:
∫ 1ˣ dx = (1/(x+1))x^(1+1) + C
= (1/(x+1))x² + C

So the final answer is: ∫ bˣ dx = (1/(x+1))x² + C, where C is the constant of integration

To integrate ∫ bˣ dx, where b is a constant, we can follow the following steps:

Step 1: Write down the integral
∫ bˣ dx

Step 2: Simplify the integral
Since b is a constant, we can treat it as such during integration, so the integral becomes:
∫ bˣ dx = b ∫ 1ˣ dx

Step 3: Integrate the function
Using the power rule of integration, where the integral of x^n is (1/(n+1))x^(n+1), we can integrate ∫ 1ˣ dx as follows:
∫ 1ˣ dx = (1/(x+1))x^(1+1) + C
= (1/(x+1))x² + C

So the final answer is: ∫ bˣ dx = (1/(x+1))x² + C, where C is the constant of integration.

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