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Antiderivative is the opposite method of thederivative method of a function and hence the name.

Antiderivative of trig functions is the method of finding the integral of the trigonometric functions which include

functions like sinx, cosx, tanx, etc.

The antiderivative notation of the given trigonometric function is:

We can use u-substitution method to find its antiderivative.

Let u = 4x, then du = 4dx, dx = du/4

Now substitute the above ‘u’ value in the given function

We get, ∫cos4x dx = ∫cosu * du/4 = 1/4 ∫cosu du

Applying the above formula, we get: 1/4∫cosu du= 1/4(sinu) + c = 1/4(sin4x) + c

The antiderivative notation of the given trigonometric function is:

We can use u-substitution method to find its antiderivative.

Now substitute the above ‘u’ value in the given function

We get, ∫2sinx cosxdx = 2 ∫u cosx * du/cosx

Cancelling ‘cosx’ up and down we get: 2 ∫u du

Applying the above formula, we get: 2 ∫udu = 2(u