Integrate $\int x\sqrt{2\sin\left(x\right)^2+2\cos\left(x\right)^2}dx$

Find the integral

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

Find the integral

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

Find the integral

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

Find the integral

$\int\sqrt[4]{x}dx$

Find the integral

$\int2x\sqrt{3-2x^2}dx$

Find the integral

$\int x^{-\frac{1}{3}}dx$

Find the integral

$\int x\sqrt{1+5x^2}dx$