sin$($ax$)$cos$($bx$)$dx $=1$ b$2$a$2$ bsin$($ax$)$sin$($bx$)+$acos$($ax$)$cos$($bx$)+$C where a and b are constants such that a$2$ b$2.($a$)$ Use the Product Identity for sine and cosine to rewrite the integrand. $($b$)$ Use u$-$substitution to evaluate the integral. $($c$)$ Use the Sum and Di

erence Identities for sine and cosine to rewrite the antiderivative and get the above integral identity. $($d$)$ Why does this formula require that a$2$ b$2?($e$)$ Give a similar formula for the integral sin$($ax$)$cos$($bx$)$dx in the case that a$2=$ b$2.($Hint: consider two cases; a $=$ b and a $=$b$.$