Prove the trigonometric identity $\cos\left(x\right)^4+\sin\left(x\right)^2+\sin\left(x\right)^2\cos\left(x\right)^2=1$

Find the integral

$\int12x^5dx$

Find the integral

$\int\left(\frac{\cos\left(x\right)}{x}\right)dx$

Find the integral

$\int\left(x^3+2\right)^23x^2dx$

Find the integral

$\int\frac{cos\left(x\right)}{x}dx$

Find the integral

$\int x^n\cdot\cos\left(x\right)dx$

Find the integral

$\int\frac{\arctan\left(x\right)}{x}dx$

Find the integral

$\int\left(x\right)\:dx$