Maths Answer the following questions in short.

$\int_{-2}^3|x-2| d x$

$\int_0^4\left[\sqrt{x^2+2 x+3}\right]^{-1} d x$

$\int_0^{\pi / 2} x \cdot \sin x \cdot d x$

$\int_0^1 \frac{1}{\sqrt{3+2 x-x^2}} \cdot d x$

$\int_0^1 \frac{x^2-2}{x^2+1} \cdot d x$

$\int_0^{\pi / 4} \cot ^2 \cdot d x$

$\int_{-3}^3 \frac{x^3}{9-x^2} \cdot d x$