$2\:\int\:2x\:^3\sqrt{3+3x^4}dx$

$42+\left(4\cdot3\right)-\left(5\cdot7\right)$

$\frac{1+\cos\left(x\right)+\sin\left(x\right)}{1-\sin\left(x\right)+\cos\left(x\right)}=\frac{1+\sin\left(x\right)}{\cos\left(x\right)}$

$\frac{1}{4}x=8$

$\left(3a\:\:b^2-2b^2\right)^3$

$\left(y+4\right)y'=2xy+4y$

$\lim\:_{x\to\:0\:}\left(\frac{1+x}{2x+1}\right)^{\frac{2x+3}{x}}$