Derivative of tan^-1(f(x)) is a factor: substitute t = tan^-1(f(x))

1. A.
   $4e^{\tan^{- 1}2x} + c$, where c is the constant of integration
2. B.
   $e^{\tan^{- 1}2x} + c$, where c is the constant of integration
3. C.
   $\frac{e^{\tan^{- 1}2x}}{2} + c$, where c is the constant of integration
4. D.
   $\ 2e^{\tan^{- 1}2x} + c$, where c is the constant of integration

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1. A.
   $\frac{\sin\left( \tan^{- 1}x^{5} \right)}{5} + c$, where c is the constant of integration
2. B.
   $x^{4}\sin\left( \tan^{- 1}x^{5} \right) + c$, where c is the constant of integration
3. C.
   $\frac{\sin\left( \tan^{- 1}x^{5} \right)}{4} + c$, where c is the constant of integration
4. D.
   $\cos\left( \tan^{- 1}x^{5} \right) + c$, where c is the constant of integration

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1. A.
   $\dfrac{1}{4}\cos(\tan^{-1}(x^4)) + c$
2. B.
   $\dfrac{1}{4}\sin(\tan^{-1}(x^4)) + c$
3. C.
   $\dfrac{1}{4}\sec(\tan^{-1}(x^4)) + c$
4. D.
   $-\dfrac{1}{4}\cos(\tan^{-1}(x^4)) + c$

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