Compute the indefinite integral
L=∫sin5(x)cos(x)dx.
a) Propose an expression u(x) that converts the integrand to a monomial in u. Justify your proposal by explicitly relating du to the original differential dx.
b) Complete the change of variable and evaluate L, showing each intermediate algebraic step until the antiderivative is obtained in terms of x.
c) Verify your result by differentiating your antiderivative and demonstrating that it reproduces the original integrand.