Solve the differential equation $3\ln\left(y\cdot dy\right)=xe^xdx$

Find the integral

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

Find the integral

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

Find the integral

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

Find the integral

$\int\frac{dx}{\sqrt{25-9x^2}}$

Find the integral

$\int\frac{\sqrt{x^2+4}}{x^4}dx$

Find the integral

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

Find the integral

$\int\frac{x}{\sqrt{49+x^2}}dx$