1
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x+\cos x}{1-\sin x} d x= $$

A

$x \tan \left(\frac{\pi}{4}+\frac{x}{2}\right)+C$

B

$x \tan \frac{x}{2}+C$

C

$x \cot \frac{x}{2}+C$

D

$x \cot \left(\frac{\pi}{4}+\frac{x}{2}\right)+C$

2
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{1}{(x+2) \sqrt{x^2+x+2}} d x=$

A

$-\frac{1}{2} \sinh ^{-1}\left(\frac{2-3 x}{\sqrt{7}(x+2)}\right)+C$

B

$-\frac{1}{2} \sin ^{-1}\left(\frac{2+3 x}{\sqrt{7}(x+2)}\right)+C$

C

$\frac{1}{2} \cosh ^{-1}\left(\frac{2+3 x}{\sqrt{7}(x+2)}\right)+C$

D

$-\frac{1}{2} \cos ^{-1}\left(\frac{2-3 x}{\sqrt{7}(x+2)}\right)+C$

3
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_{-4}^5 \frac{1}{\sqrt{20+x-x^2}} d x= $$

A

$\frac{81 \pi}{8}$

B

$\frac{9 \pi}{2}$

C

$\pi$

D

$\frac{\pi}{10}$

4
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int_0^{\frac{\pi}{2}} \frac{d x}{\cos x-\sqrt{3} \sin x}= $$

A

0

B

$\frac{1}{2} \log (2-\sqrt{3})$

C

$\frac{1}{2} \log (2+\sqrt{3})$

D

$\frac{1}{2} \log (2 \sqrt{3}-3)$

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