Find the limit of $2x^7\arctan\left(x\right)-\pi x^7$ as $x$ approaches $\infty $

Find the integral

$\int\:\:x\sqrt{1+x^2}dx$

Find the integral

$\int x\sqrt[3]{3-x^2}dx$

Find the integral

$\int\sqrt{1\:-\:x^2}dx$

Find the integral

$\int\sqrt{1-7w^2}dw$

Find the integral

$\int x^2\sqrt{x^2-4}dx$

Find the integral

$\int2x\sqrt{x^2+1}dx$

Find the integral

$\int\sqrt{5x+3}dx$