1
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{d x}{12 \cos x+5 \sin x}= $$

A

$\frac{1}{13} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}-\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

B

$\frac{5}{12} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}-\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

C

$\frac{1}{13} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}+\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

D

$\frac{5}{12} \log \left|\tan \left(\frac{\pi}{4}+\frac{x}{2}+\frac{1}{2} \tan ^{-1} \frac{5}{12}\right)\right|+C$

2
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{\cos ^3 x}{\sin ^2 x+\sin ^4 x} d x=c-\operatorname{cosec} x-f(x)$, then $f\left(\frac{\pi}{2}\right)=$

A

1

B

0

C

$\pi / 2$

D

$\pi$

3
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{13 \cos 2 x-9 \sin 2 x}{3 \cos 2 x-4 \sin 2 x} d x= $$

A

$3 x-\frac{1}{2} \log |3 \cos 2 x-4 \sin 2 x|+C$

B

$\frac{x}{2}-3 \log |3 \cos 2 x-4 \sin 2 x|+C$

C

$3 x+\frac{1}{2} \log |3 \cos 2 x-4 \sin 2 x|+C$

D

$x+\frac{3}{2} \log |3 \cos 2 x-4 \sin 2 x|+C$

4
AP EAPCET 2025 - 22nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \sqrt{x^2+x+1} d x $$

A

$\frac{(2 x+1)}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$

B

$\frac{x+1}{4} \sqrt{x^2+x+1}+\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$

C

$\frac{x+1}{4} \sqrt{x^2+x+1}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$

D

$\frac{(2 x+1)}{4} \sqrt{x^2+x+1}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+C$