Integral of 1 over a quadratic, or over its square root: complete the square and use the standard form

1. A.
   $\frac{1}{4}\log\frac{1+x}{7-x}+c$
2. B.
   $\frac{1}{8}\log\frac{7-x}{1+x}+c$
3. C.
   $\frac{1}{4}\log\frac{7-x}{1+x}+c$
4. D.
   $\frac{1}{8}\log\frac{1+x}{7-x}+c$

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1. A.
   $\frac{1}{4}\log\left|\frac{7+x}{1-x}\right|+c$
2. B.
   $\frac{1}{8}\log\left|\frac{7+x}{1-x}\right|+c$
3. C.
   $\frac{1}{16}\log\left|\frac{7+x}{1-x}\right|+c$
4. D.
   $\frac{1}{32}\log\left|\frac{7+x}{1-x}\right|+c$

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1. A.
   $\sin^{-1}x, \dfrac{x - a}{a}$
2. B.
   $\sin^{-1}x, \dfrac{x + a}{a}$
3. C.
   $\tan^{-1}x, \dfrac{x - a}{a}$
4. D.
   $\tan^{-1}x, \dfrac{x + a}{a}$

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1. A.
   $\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x + 5}{\sqrt{7}}\right) + c$
2. B.
   $-\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x - 5}{\sqrt{7}}\right) + c$
3. C.
   $\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x - 5}{\sqrt{7}}\right) + c$
4. D.
   $-\dfrac{2}{\sqrt{7}}\tan^{-1}\left(\dfrac{2x + 5}{\sqrt{7}}\right) + c$

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

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