sin^m x cos^n x with m + n a negative even number: divide by a power of cos x and substitute t = tan x

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

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1. A.
   25
2. B.
   14
3. C.
   16
4. D.
   20

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

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1. A.
   $f(x)=\tan^{-8/3}x$, $g(x)=\tan^{-2/3}x$
2. B.
   $f(x)=\tan^{8/3}x$, $g(x)=\tan^{-2/3}x$
3. C.
   $f(x)=\tan^{-8/3}x$, $g(x)=\tan^{2/3}x$
4. D.
   $f(x)=\tan^{8/3}x$, $g(x)=\tan^{2/3}x$

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1. A.
   $\frac{27}{10}$
2. B.
   $\frac{16}{5}$
3. C.
   $\frac{27}{5}$
4. D.
   $\frac{21}{5}$

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1. A.
   $-\frac{4}{7}\tan^{-4/7}x + c$
2. B.
   $\frac{4}{7}\tan^{4/7}x + c$
3. C.
   $-\frac{7}{4}\tan^{-4/7}x + c$
4. D.
   $\frac{7}{4}\tan^{4/7}x + c$

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1. A.
   $2\sqrt{\tan x} + \frac{1}{5}(\tan x)^{5/2} + c$
2. B.
   $\sqrt{\tan x} + \frac{2}{5}(\tan x)^{5/2} + c$
3. C.
   $\frac{1}{2}\sqrt{\tan x} + \frac{2}{5}(\tan x)^{5/2} + c$
4. D.
   $2\sqrt{\tan x} + \frac{1}{5}(\tan x)^{5/2} + c$

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

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1. A.
   $2\sqrt{\sec x} + c$, where c is a constant of integration
2. B.
   $2\sqrt{\tan x} + c$, where c is a constant of integration
3. C.
   $\frac{2}{\sqrt{\tan x}} + c$, where $c$ is a constant of integration
4. D.
   $\frac{2}{\sqrt{\sec x}} + c$, where c is a constant of integration

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1. A.
   $p = \dfrac{\sqrt{2}}{5}, q = \dfrac{1}{5}$
2. B.
   $p = \dfrac{\sqrt{2}}{3}, q = 3$
3. C.
   $p = \dfrac{\sqrt{2}}{5}, q = 5$
4. D.
   $p = \dfrac{2}{\sqrt{5}}, q = \sqrt{5}$

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