Finding Indefinite Integrals

In Exercises 17–...

Question

Finding Indefinite Integrals

In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫(4secx tanx − 2 sec²x)dx

Accepted Answer

Welcome back, everyone. Find the indefinite integral 62 X tangent X minus 3 sequence squared XD X. For this problem we can begin by applying the properties of integrals, and we are going to apply two properties. We're going to factor out constants and we're going to split the integral into two parts because we have a difference. So the first integral is going to become 6. We can factor out the constant multiplied by the integral of s and X. Ancient acts DX and we're going to subtract 3 multiplied by the integral of c squared XDX. Now, let's recognize that each integral is an elementary integral. The integral of sequent X tangent XDX is equal to sequent X. We're going to add a constant of integration C1, and the integral of squared XD X is tangent X. We're going to add the constant of integration C2. So now we can evaluate our integral. It is equal to 6 multiplied by C X plus 6 multiplied by C1, we can ignore that for now. We will just have a combination of constants. For the next function, we are subtracting 3 multiplied by tangent X. Minus 3C2. So essentially, the combination of those constants is just going to result in some constant of integration C. And that's our final answer. 62 X minus 3 tangent X plus C. Thank you for watching.

Finding Indefinite IntegralsIn Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.∫(4secx tanx − 2 sec²x)dx

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Finding Indefinite Integrals

In Exercises 17–56, find the most general antiderivative or indefinite integral. You may need to try a solution and then adjust your guess. Check your answers by differentiation.

∫(4secx tanx − 2 sec²x)dx