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

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1. A
   $\dfrac{1}{(n-1)(1+\ln x)^{n-1}} + c$
2. B
   $\dfrac{1-n}{(1+\ln x)^{1-n}} + c$
3. C
   $\dfrac{n+1}{(1+\ln x)^{n+1}} + c$
4. D
   $-\dfrac{1}{(n-1)(1+\ln x)^{n-1}} + c$

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1. A
   $\dfrac{dy}{dx} = 4xy^{2}$
2. B
   $\dfrac{dy}{dx} = \dfrac{1}{y}$
3. C
   $\dfrac{dy}{dx} = x^{2}y$
4. D
   $\dfrac{dy}{dx} = -4xy^{2}$

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1. A
   $e^{x}\tan y\,dx + (1-e^{x})\,dy = 0$
2. B
   $e^{x}\tan y\,dx + (1-e^{x})\sec^{2}y\,dy = 0$
3. C
   $e^{x}(1-e^{x})\,dx + \tan y\,dy = 0$
4. D
   $e^{x}\tan y\,dy + (1-e^{x})\,dx = 0$

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1. A
   $\sin x \cdot 2^{(\sin x)^{2}}\ln 4$
2. B
   $2\sin x \cdot 2^{(\sin x)^{2}}\ln 4$
3. C
   $\ln(\sin x)\cdot 2^{(\sin x)^{2}}$
4. D
   $2\sin x\cos x \cdot 2^{(\sin x)^{2}}$

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1. A
   $\dfrac{1}{4}$
2. B
   $\dfrac{1}{2}$
3. C
   1
4. D
   2

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1. A
   $\dfrac{2}{3}$ square units
2. B
   $\dfrac{4}{3}$ square units
3. C
   $\dfrac{1}{3}$ square units
4. D
   1 square unit

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1. A
   $T = (-\infty, 2) \cup (3, \infty)$ and $S = (2, 3)$
2. B
   $T = \phi$ and $S = (-\infty, \infty)$
3. C
   $T = (-\infty, \infty)$ and $S = \phi$
4. D
   $T = (2, 3)$ and $S = (-\infty, 2) \cup (3, \infty)$

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