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1
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{x^4+1}{x^2+1} d x=A x^3+B x^2+C x+D \tan ^{-1} x+E$, then $A+B+C+D=$

A

$\frac{3}{2}$

B

$\frac{4}{3}$

C

$\frac{1}{3}$

D

$\frac{2}{3}$

2
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \begin{aligned} & \text { If } \int \frac{x^2-x+2}{x^2+x+2} d x=x-\log (f(x))+\frac{2}{\sqrt{7}} \tan ^{-1}(g(x))+c, \text { then } \\ & f(-1)+\sqrt{7} g(-1)= \end{aligned} $$

A

1

B

0

C

-1

D

2

3
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \sec \left(x-\frac{\pi}{3}\right) \sec \left(x+\frac{\pi}{6}\right) d x= $$

A

$\log \left|\frac{\sec \left(x-\frac{\pi}{3}\right)}{\sec \left[x+\frac{\pi}{6}\right]}\right|+C$

B

$\log \left|\frac{\cos \left(x-\frac{\pi}{3}\right)}{\cos \left(x+\frac{\pi}{6}\right)}\right|+C$

C

$\log \left|\frac{\operatorname{cosec}\left(x-\frac{\pi}{3}\right)}{\operatorname{cosec}\left(x+\frac{\pi}{6}\right)}\right|+C$

D

$\log \left|\frac{\sin \left(x-\frac{\pi}{3}\right)}{\sin \left(x+\frac{\pi}{6}\right)}\right|+C$

4
AP EAPCET 2025 - 26th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int \frac{a \cos x+3 \sin x}{5 \cos x+2 \sin x} d x=\frac{26}{29} x-\frac{k}{29} \log |5 \cos x+2 \sin x|+\ldots$ then $|a+k|=$

A

3

B

11

C

12

D

2

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