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(1) Evaluate `int cos^5 x dx`.
Hint: Express `cos^4 x` in terms of `sin x`. Then use the substitution `u=sin x`. Back substitute to write your soluton in terms of `x`.
solution `=`
`+ C`
(2) Evaluate `int cos^2 x dx`.
Hint: Use the half-angle identity `cos^2 x = 1/2 (1+cos 2x)`.
solution `=`
`+ C`
`1/5 (sin(x))^5 -2/3 (sin(x))^3 + sin(x)`
`x/2 + (sin(2x))/4`