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different rules like Power rule, Substitution rues etc. and the antiderivative of the function is calculated.

Antiderivative of trig functions is finding the integral of any trigonometric function. Different techniques are

used in order to get the solution of antiderivative of the trigonometric functions.

The antiderivative notation of the given trigonometric function is:

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

Let u = 3x, then du = 3dx, dx = du/3

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

We get, ∫sin3x dx = ∫sinu * du/3 = 1/3 ∫sinu du

Applying the above formula, we get: 1/3∫sinu du = 1/3(-cosu) + c = -1/3(cos3x) + c

The antiderivative notation of the given trigonometric function is:

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

Let u = 2x, then du = 2dx, dx = du/2

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

We get, ∫sec2x tan2x dx = ∫secutanu * du/2 = 1/2 ∫secutanu du

Applying the above formula, we get: 1/2∫secu tanu du = 1/2(secu) + c = 1/2(sec2x) + c