The value of $\int_{-1}^1 \sin ^5 \mathrm{x} \cos ^4 \mathrm{xdx}$ is

$$ \text { The value of } \int_0^{2 \pi} \sqrt{1+\sin \left(\frac{x}{2}\right)} d x \text { is } $$

$\int_0^1 \log \left(\frac{1}{x}-1\right) d x$ is

$\int_{-\pi}^\pi\left(1-x^2\right) \sin x \cdot \cos ^2 x d x$ is