Question

Evaluate using u-substitution:

Integral of: 4x(tan(x^2))dx

Integral of: (1/(sqrt(x)*x^(sqrt(x))))dx

Integral of: (cos(lnx)/x)dx

Answer 1

Integral of: (cos(lnx)/x)dx
let u = ln x
du = dx/x
Your integral is therefore that of
cos u du, which is sin u = sin(ln x)

Try the others yourself. In the first one, I would let x^2 = u

Answer 2

Integral 3x/x2(x-2)dx