What is the antiderivative of the function y=(e^sinx)*cosx?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To determine the antiderivative of the given function, we'll have to evaluate the indefinite integral.

We can use the substitution technique to evaluate the indefinite integral.

Let sin x be t.

sin x = t

We'll differentiate both sides and we'll get:

cos x*dx = dt

We'll re-write the integral, changing the x variable:

Int (e^sin x)*cos x dx  = Int e^t*dt

Int e^t*dt = e^t + C

The requested antiderivative of the function y =(e^sin x)*cos x  is: Y =  [e^(sin x)] + C