1. A
   $\frac{1}{2}\sqrt{x+1}+c$
2. B
   $\frac{2}{3}(x+1)^{3/2}+c$
3. C
   $\sqrt{x+1}+c$
4. D
   $2(x+1)^{3/2}+c$

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1. A
   $\log x - f(x)+c$
2. B
   $f(x)+\log x+c$
3. C
   $f(x)-\log x+c$
4. D
   $\frac{1}{5}x^5 f(x)+c$

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1. A
   $\log(3x)-\log(9x)+c$
2. B
   $\log(x)-(\log 3)\cdot\log(\log 9x)+c$
3. C
   $\log 9-(\log x)\cdot\log(\log 3x)+c$
4. D
   $\log(x)+(\log 3)\cdot\log(\log 9x)+c$

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

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

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1. A
   $x\cot\left(\frac{x}{2}\right)+c$
2. B
   $-x\cot\left(\frac{x}{2}\right)+c$
3. C
   $\cot\left(\frac{x}{2}\right)+c$
4. D
   $x\tan\left(\frac{x}{2}\right)+c$

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

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1. A
   $(5, 3)$
2. B
   $(3, 5)$
3. C
   $\left(\frac{1}{5},\frac{1}{3}\right)$
4. D
   $(4, 4)$

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1. A
   $\log(\csc x-\cot x)+\tan\left(\frac{x}{2}\right)+c$
2. B
   $\sin 2x-\cos x+c$
3. C
   $\log(\sec x+\tan x)-\cot\left(\frac{x}{2}\right)+c$
4. D
   $\cos 2x-\sin x+c$

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1. A
   $2\sqrt{\cot x}+c$
2. B
   $-2\sqrt{\cot x}+c$
3. C
   $\frac{1}{2}\sqrt{\cot x}+c$
4. D
   $\sqrt{\cot x}+c$

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1. A
   $\frac{e^x}{x}+c$
2. B
   $\frac{e^x}{x^2}+c$
3. C
   $\left(x-\frac{1}{x}\right)e^x+c$
4. D
   $xe^{-x}+c$

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1. A
   $\frac{x}{2}[\sin(\log x)-\cos(\log x)]+c$
2. B
   $\frac{x}{2}[\sin(\log x)+\cos(\log x)]+c$
3. C
   $\frac{x}{2}[\cos(\log x)-\sin(\log x)]+c$
4. D
   $\frac{x}{4}[\cos(\log x)-\sin(\log x)]+c$

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1. A
   $\frac{1}{2}(1+\log x)^2+c$
2. B
   $x^{2x}+c$
3. C
   $x^x\log x+c$
4. D
   $x^x+c$

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