Day 246: MHT-CET Maths

1. A.
   $\sqrt{2}\log\left|\tan\!\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|+c$
2. B.
   $\frac{1}{\sqrt{2}}\log\left|\tan\!\left(\frac{x}{2}+\frac{\pi}{8}\right)\right|+c$
3. C.
   $\frac{1}{\sqrt{2}}\log\left|\frac{\tan(x/2)-(\sqrt{2}+1)}{\tan(x/2)+(\sqrt{2}-1)}\right|+c$
4. D.
   $-\frac{1}{\sqrt{2}}\log\left|\frac{\tan(x/2)-(\sqrt{2}+1)}{\tan(x/2)+(\sqrt{2}-1)}\right|+c$

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1. A.
   $3.232$
2. B.
   $2.221$
3. C.
   $3.333$
4. D.
   $2.222$

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1. A.
   $2n\pi \pm \frac{\pi}{3},n \in \mathbb{Z}$
2. B.
   $n\pi + \frac{\pi}{3},n \in \mathbb{Z}$
3. C.
   $n\pi + \frac{\pi}{4},n \in \mathbb{Z}$
4. D.
   $\ 2n\pi \pm \frac{\pi}{6},n \in \mathbb{Z}$

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1. A.
   $\dfrac{1}{6}$
2. B.
   $-\dfrac{1}{12}$
3. C.
   $-\dfrac{1}{6}$
4. D.
   $\dfrac{1}{12}$

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

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