Substitute first, then use the integral of e^t [f(t) + f'(t)] = e^t f(t)

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

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

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

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1. A.
   $e^{f(x)}(-\mathrm{\csc}\,x - x) + c$
2. B.
   $e^{f(x)}(\mathrm{\csc}\,x + x) + c$
3. C.
   $e^{f(x)}(\cos x - x) + c$
4. D.
   $e^{f(x)}(\cot^2 x + x) + c$

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

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

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