QuestionEvaluate $\int_{0}^{1} \frac{y \ln ^{4}\left(y^{2}+1\right)}{y^{2}+1} d y$

Studdy Solution
Compute the definite integral:
$$\frac{1}{2} \left( \frac{\ln^5(2)}{5} - \frac{\ln^5(1)}{5} \right)$$
Since $\ln(1) = 0$, the expression simplifies to:
$$\frac{1}{2} \cdot \frac{\ln^5(2)}{5} = \frac{\ln^5(2)}{10}$$
The value of the integral is:
$$\boxed{\frac{\ln^5(2)}{10}}$$