Antiderivative Trig Functions Antiderivative Trig Functions The definition of antiderivative is, ∫ g (x) dx = f(x )+ c, where d f(x) /dx = g(x). The following are the integrals of the trigonometric functions. Following are the integrals or antiderivatives of the sin, cos, tan, cot, cosec etc. functions. For general if the sin x is a trigonometric function then cos x is the derivative of that function. Antiderivatives of some of the sin function are as follows- ∫ sin ax = - (1/a) cos ax + c ∫ sin n ax dx = - sin (n-1) . ax . cos ax / na + (n-1 )/ n . ∫ sin n-2 ax dx ( for n > 2 ) Antiderivative of the two cos functions are as following- ∫ cos ax dx = (1/a) sin ax +c ∫ cosn ax dx = cos n-1 ax . sin ax / na + ( n-1 / n ) . ∫ cos n-2 ax dx Know More About Antiderivative of 0
(for n > 0) Integral of the tan x is defined as the formula below ∫ tan ax dx = -( 1 / a ) log ( cos ax ) + c Antiderivative of the \secant function is defined as follows- ∫ sec ax dx = ( 1 / a ) log (sec ax + tan ax ) + c Integral of the cosec x is as follows- ∫ cosec ax dx = -( 1 / a ) log (cosec ax + cot ax ) + c Integral of the cot x is as follows- ∫ cot ax dx = ( 1 / a ) sin ax +c Here c is the integral constant in all the trigonometric functions defined above and a is a constant and n is the positive integral.
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