Obtain the reduction formula for `intcos^(n)xdx`

intcos^(2) x dx

intcos^5x dx

intcos^2n x\ dx

intcos^8xsinxdx

intcos(logx)/xdx

intcos^-1(1/x)dx

Deduce the reduction formula for I_(n)=int(dx)/(1+x^(4))^(n) and Hence evaluate I_(2)=int(x)/(1+x^(4))^(2) .

intcos^(3)x" " dx=

Obtain the dimensional formula for the Poisson's ratio.

intcos^4 2x\ dx