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

3 Answers

  • 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!

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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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