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The given integral is:

\[
I = \int_0^1 t^4 (1 - t)^3 \, dt
\]

This integral represents a Beta function, which is generally defined as:

\[
B(x, y) = \int_0^1 t^{x-1} (1 - t)^{y-1} \, dt
\]

By comparing the given integral with the general form of the Beta function, we can identify:

\[
x - 1 = 4 \quad \text{so} \quad x = 5
\

This integral problem evaluates the Beta function for x = 5 and y = 4. Learn how to calculate this integral step-by-step using key calculus concepts and the Beta function formula. Suitable for university-level calculus students.

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