Question
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.$$\int\left(2+\tan ^{2} \theta\right) d \theta$$
Step 1
We can rewrite this integral using the trigonometric identity $1+\tan^2\theta=\sec^2\theta$. This gives us $\int\left(1+\sec ^{2} \theta\right) d \theta$. Show more…
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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. $$\begin{array}{l}{\int\left(1+\tan ^{2} \theta\right) d \theta} \\ {\left(\operatorname{Hint} : 1+\tan ^{2} \theta=\sec ^{2} \theta\right)}\end{array}$$
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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. $$\int \frac{2}{5} \sec \theta \tan \theta d \theta$$
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. $$\begin{array}{l}{\int\left(1+\tan ^{2} \theta\right) d \theta} \\ {\text { (Hint: } 1+\tan ^{2} \theta=\sec ^{2} \theta )}\end{array}$$
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