Integrand with sqrt(x) or sqrt(x - a): substitute x = t^2 (or x - a = t^2, x = t^6)

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

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1. A.
   $-\frac{\pi}{6}+\frac{1}{2}+\frac{\sqrt{3}}{4}$
2. B.
   $-\frac{\pi}{12}+\frac{1}{2}+\frac{\sqrt{3}}{4}$
3. C.
   $\frac{\pi}{6}+\frac{1}{2}-\frac{\sqrt{3}}{4}$
4. D.
   $\frac{\pi}{12}+\frac{1}{2}-\frac{\sqrt{3}}{4}$

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1. A.
   $\log\sqrt{x} + c$, where c is the constant of integration.
2. B.
   $\ \log(\sqrt{x} + x) + c$, where c is the constant of integration.
3. C.
   $\log(1 + \sqrt{x}) + c$, where c is the constant of integration.
4. D.
   $2\log(1 + \sqrt{x}) + c$, where c is the constant of integration.

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1. A.
   $2, - 3,6, - 6$
2. B.
   $2,3, - 6,6$
3. C.
   $2, - 3, - 6,6$
4. D.
   $- 2, - 3,6,6$

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

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

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