(x-3)(x+5)dx

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Jun 03, 2024

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Integral of (x-3)(x+5)dx

In this article, we will discuss the integral of the algebraic expression (x-3)(x+5)dx.

Expanding the Expression

Before we integrate, let's expand the given expression using the distributive property:

(x-3)(x+5) = x^2 + 2x - 15

Now, we can rewrite the integral as:

∫(x^2 + 2x - 15)dx

Integrating the Expression

To integrate the expression, we will integrate each term separately:

∫x^2 dx = (1/3)x^3 + C

∫2x dx = x^2 + C

∫-15 dx = -15x + C

Now, we can combine the results:

∫(x^2 + 2x - 15)dx = (1/3)x^3 + x^2 - 15x + C

Final Answer

The integral of (x-3)(x+5)dx is:

(1/3)x^3 + x^2 - 15x + C

where C is the constant of integration.

Note: The constant of integration C can take on any value, and it is determined by the specific problem or application.