Simplificar la expresión trigonométrica $\sin\left(\frac{\pi }{3}\right)-\cos\left(\frac{\pi }{6}\right)$

Calcular la integral

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

Calcular la integral

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

Calcular la integral

$\int x^2\cdot e^2dx$

Calcular la integral

$\int\left(8x-12\right)\left(4x^2-12x\right)^4dx$

Calcular la integral

$\int bx^3dx$

Calcular la integral

$\int3ay^2dy$

Calcular la integral

$\int a\:dx$