Calculus 2

Evaluate $\displaystyle \int \frac{x \, sin^{-1}x}{\sqrt{1-x^2}} \, dx$

Evaluate$\displaystyle \int e^{cos^{-1}x}\, dx$

Evaluate $\displaystyle \int \frac{sin(\frac{1}{x})}{x^3} \, dx$

Evaluate $\displaystyle \int tan^{-1} \, \sqrt{x} \, dx$

Given $x = -y^2 + 4y$, find the arc length from $y = 0$ to $y = 4$ and the surface area when the arc is rotated about the x-axis and y-axis.

Evaluate the integral $\displaystyle \int_{-\infty}^{\infty} e^{x^2} \, dx$.