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Antiderivative of Cos(3x)?

could someone explain the rule or formula for how to take the antiderivative of say Cos(3x) or -Sin(2x). Also what about Sin(x^2) {sin x squared]? thanks
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Akeem Kemmer MD

Feb 20, 2025

d/dx( sin nx) = n*cos(nx)Thus the anti-derivative of cos(nx) is (1/n)*sin(nx)Thus anti-derivative of cos(3x) is (1/3)sin(3x) Similarly d/dx(cos nx)= – n*sin(nx) (Note the minus sign)Thus anti-derivative of n*sin(nx) is -cos(nx)or anti-derivative of sin(nx) is -(1/n)cos(nx)Thus anti-derivative of -sin 2x is +(1/2) cos(2x)To do the sin of x^2 you are on your own. If can find the anti-derivative of sin(x squared) please tell us as it is not do-able without defining new functions!... Show More
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Akeem Kemmer MD

Feb 20, 2025

This Site Might Help You.RE:Antiderivative of Cos(3x)?could someone explain the rule or formula for how to take the antiderivative of say Cos(3x) or -Sin(2x). Also what about Sin(x^2) {sin x squared]? thanks... Show More
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