Question

Is my work wrong?

Answer 1

\[\int\limits_{}^{}(\cos(x)+\sin(x)^2(\cos(2x)) dx\]

\[\int\limits_{}^{}(\cos^2(x)+2\sin(x)\cos(x)+\sin^2(x))(\cos(2x))dx\]

\[\int\limits_{}^{}(1+\sin(2x))(\cos(2x)) dx\]

u=1+sin(2x)

dy/2=cos(2x) dx

\[\frac{ 1 }{ 2 } \int\limits_{}^{}udu\]

\[\frac{ 1 }{4 } (u^2+C)\]

\[\frac{ 1 }{ 4 }(1+\sin(2x))^2+C\]

Answer 2

dy/2=cos(2x) dx should say du/2 sorry :P .

Answer 3

@chihiroasleaf

Answer 4

yupp..., correct... :)

Answer 5

Sorry the First Intergal should be this: