Solving an Integral Step by Step
The image shows an integral that needs to be solved. Let's solve the integral step by step:
The integral is \( \int (8x^3 - x^2 + 5x - 1) \,dx \).
To solve it, we will integrate each term separately:
1. The integral of \( 8x^3 \) with respect to x is \( \frac{8}{4}x^4 \) or \( 2x^4 \).
2. The integral of \( -x^2 \) with respect to x is \( -\frac{1}{3}x^3 \).
3. The integral of \( 5x \) with respect to x is \( \frac{5}{2}x^2 \).
4. The integral of \( -1 \) with respect to x is \( -x \).
Putting it all together, we get:
\[ \int (8x^3 - x^2 + 5x - 1) \,dx = 2x^4 - \frac{1}{3}x^3 + \frac{5}{2}x^2 - x + C \]
where \( C \) is the constant of integration.
