https://file.aiquickdraw.com/mathbot/file/1725857035138zfxb08ii.jpg

It seems that the optical character recognition (OCR) did not correctly interpret the image. However, I can clearly see the expression in the image provided.

The integral is:

\[
\int_0^1 \frac{3x^3 - x^2 + 2x - 4}{\sqrt{x^2 - 3x + 2}} \, dx
\]

Let's proceed to solve it step by step.

First, we need to simplify the denominator \(\sqrt{x^2 - 3x + 2}\).

### Factorizing the denominator:

\[
x^2 - 3x + 2 = (x - 1)(x - 2)
\]

Thus, the integral becomes:

\[
\int_0^1 \frac{3x^3 - x^2 + 2x - 4}{\sqrt{(x - 1)(x - 2)}} \, dx
\]

Next, we will proceed with solving this integral.

Solve the integral of (3x^3 - x^2 + 2x - 4) / sqrt(x^2 - 3x + 2) from 0 to 1.

Find the integral of (3x^3 - x^2 + 2x - 4) / sqrt(x^2 - 3x + 2) from 0 to 1 with a step-by-step solution. This problem covers integration techniques, algebraic fractions, and square root simplification. Suitable for Grades 11-12 or early college students.

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