Find the derivative using logarithmic differentiation method $\left(a^2+\left(a+x\right)^2\right)\left(\left(a+x\right)^2+\left(a+2\right)^2\right)$

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

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