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1
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{x^4+1}{x^6+1} d x=$
A
$\tan ^{-1} x-\tan ^{-1} x^3+c$
B
$\tan ^{-1} x-\frac{1}{3} \tan ^{-1} x^3+c$
C
$\tan ^{-1} x+\tan ^{-1} x^3+c$
D
$\tan ^{-1} x+\frac{1}{3} \tan ^{-1} x^3+c$
2
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$\int e^x(x+1)^2 d x=$
A
$x e^x+c$
B
$e^x x^2+c$
C
$e^x\left(x^2+1\right)+c$
D
$e^x(x+1)+c$
3
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\frac{1}{(3 x+1)(x-2)}=\frac{A}{3 x+1}+\frac{B}{x-2}$ and $\frac{x+1}{(3 x+1)(x-2)}=\frac{C}{3 x+1}+\frac{D}{x-2}$, then

A

$A+3 B=0, A: C=1: 3, B: D=2: 3$

B

$A+3 B=0, A: C=3: 1, B: D=3: 2$

C

$A-3 B=0, A: C=3: 2, B: D=1: 3$

D

$A+3 B=0, A: C=3: 2, B: D=1: 3$

4
AP EAPCET 2024 - 21th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $x \in\left[2 n \pi-\frac{\pi}{4}, 2 n \pi+\frac{3 \pi}{4}\right]$ and $n \in Z$, then $\int \sqrt{1-\sin 2 x} d x=$
A
$-\cos x+\sin x+c$
B
$\cos x+\sin x+c$
C
$-\cos x-\sin x+c$
D
$\cos x-\sin x+c$
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