Kailey VonRueden
Nov 05, 2024
Antiderivative of Cos(3x)?
Could someone explain the rules or formulas for finding the antiderivative of functions like cos(3x) and -sin(2x)? Additionally, how would one approach the antiderivative of sin(x²)? Thank you!
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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