It looks like you're presenting an integral equation, but the formatting might be a bit unclear. Let me break it down and clarify the expression to help with solving it.

From what I understand, this equation looks like an indefinite integral:

$\int (6x^5 - 4x^4 + 2x^3 - x^2 + 1) \, dx$

Where the expression inside the integral is:

$6x^5 - 4x^4 + 2x^3 - x^2 + 1$

You also mentioned a constant $C$, which is common for indefinite integrals.

To solve the integral, we'll integrate each term separately. Here's the step-by-step process:

Step 1: Integrate each term

$\int 6x^5 \, dx = \frac{6x^6}{6} = x^6$ $\int -4x^4 \, dx = \frac{-4x^5}{5} = -\frac{4x^5}{5}$ $\int 2x^3 \, dx = \frac{2x^4}{4} = \frac{x^4}{2}$ $\int -x^2 \, dx = \frac{-x^3}{3}$ $\int 1 \, dx = x$

Step 2: Combine the results

So the integral becomes: $x^6 - \frac{4x^5}{5} + \frac{x^4}{2} - \frac{x^3}{3} + x + C$

Thus, the solution to your integral is:

$\int (6x^5 - 4x^4 + 2x^3 - x^2 + 1) \, dx = x^6 - \frac{4x^5}{5} + \frac{x^4}{2} - \frac{x^3}{3} + x + C$

Let me know if you'd like further clarification or have any other questions!

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Tip: When solving integrals, always remember to apply the power rule for polynomials and keep track of the constants for each term.