Find the derivative of $x<y<0$ using the definition

Find the integral

$\int x^3sin\left(x\right)dx$

Find the integral

$\int\left(3x^2+1\right)^6dx$

Find the integral

$\int12x^5dx$

Find the integral

$\int xsinx\:dx$

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

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