By using the properties of definite integrals, evaluate the integrals
`int_(0)^(pi/4)log (1 +tan x) dx`

By using the properties of definite integrals, evaluate the integrals int_(0)^(4)|x-1|dx

By using the properties of definite integrals, evaluate the integrals int_(0)^( pi)log(1+cos x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(2 pi)cos^(5)xdx

By using the properties of definite integrals, evaluate the integrals int_(-5)^(5)|x+2|dx

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(2log sin x-log sin2x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(1)x(1-x)^(n)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^( pi)(xdx)/(1+sin x)

By using the properties of definite integrals, evaluate the integrals int_(0)^(2)x sqrt(2-x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))cos^(2)xdx

By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(sin x-cos x)/(1+sin x cos x)dx