Problem: `int x^(2)cos^(2)xdx`

9. int sin^(2)x cos^(3)xdx

int cos^(2)x sin xdx

int_0^(pi/2) cos^5xdx

5. int x sec^(2)xdx

int(1+2sinx)/cos^2xdx

Consider the integrals I_(1)=overset(1)underset(0)inte^(-x)cos^(2)xdx,I_(2)=overset(1)underset(0)int e^(-x^(2))cos^(2)x dx,I_(3)=overset(1)underset(0)int e^(-x^(2//2))cos^(2)xdx and I_(4)=overset(1)underset(0)int e^(-x^(2//2))dx . The greatest of these integrals, is

(i) int cos^(4)xdx

solve int e^(tan x)sec^(2)xdx

int_0^pi xcos^2xdx

(1) int_(0)^( 2pi)cos^(7)xdx