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ammu123
 2 years ago
integrate 6cos^3(3x)
ammu123
 2 years ago
integrate 6cos^3(3x)

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RupaBose
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits\limits{6(\cos^3 (3x)) dx}=6\int\limits\limits{(\cos^2(3x)*\cos(3x) dx}=6\int\limits\limits{(1\sin^2(3x))(\cos (3x) dx}=6\int\limits\limits{\cos(3x)\sin^2(3x)\cos(3x) dx}=6[\frac{ \sin(3x) }{ 3 } \int\limits{\sin^2(3x)\cos(3x) dx]=2\sin (3x)6[\frac{\sin^3(3x)}{9}]+C=2\sin(3x)+\frac{2}{3}\sin^2(3x)+C}\]

RupaBose
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits\limits\limits{6(\cos^3 (3x)) dx}=6\int\limits\limits\limits{(\cos^2(3x)*\cos(3x) dx}\] \[=6\int\limits\limits\limits\limits\limits{(1\sin^2(3x))(\cos (3x) dx}\] \[=6\int\limits\limits\limits{\cos(3x)\sin^2(3x)\cos(3x) dx}\] \[=6[\frac{ \sin(3x) }{ 3 } \int\limits\limits{\sin^2(3x)\cos(3x) dx]}\] \[=2\sin (3x)6[\frac{\sin^3(3x)}{9}]+C\] \[=2\sin(3x)+\frac{2}{3}\sin^2(3x)+C\]

MrWho
 2 years ago
Best ResponseYou've already chosen the best response.0If you couldn't find the integration just use the online integration solver and see the solution to have full grasp of the integration techniques.

sashankvilla
 2 years ago
Best ResponseYou've already chosen the best response.02⋅(sin(3x)−(sin(3x))^3/3)
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