1
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int x \tan ^{-1} \sqrt{\frac{1+x^2}{1-x^2}} d x= $$

A

$\frac{x^2}{4}\left(\pi-\cos ^{-1} x^2\right)+\frac{1}{4} \sqrt{1-x^2}+C$

B

$\frac{x^2}{4}\left(\pi-\cos ^{-1} x^2\right)+\frac{1}{4} \sqrt{1-x^4}+C$

C

$\frac{x^2}{4}\left(\pi+\cos ^{-1} x^2\right)-\frac{1}{4} \sqrt{1-x^4}+C$

D

$\frac{x^2}{4}\left(\pi+\cos ^{-1} x^2\right)-\frac{1}{4} \sqrt{1-x^2}+C$

2
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{1}{(2 \cos x+\sin x)^2} d x= $$

A

$\frac{1}{2+\tan x}+C$

B

$-\frac{1}{2 \tan x+1}+C$

C

$\frac{\cos x}{\cos x+2 \sin x}+C$

D

$-\frac{\cos x}{2 \cos x+\sin x}+C$

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

If $\frac{x+3}{(x+1)\left(x^2+2\right)}=\frac{a}{x+1}+\frac{b x+c}{x^2+2}$, then $a-b+c=$

A

0

B

1

C

3

D

2

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

$$ \int e^{-x}\left(x^3-2 x^2+3 x-4\right) d x= $$

A

$-e^{-x}\left(x^3-x^2+5 x-1\right)+C$

B

$e^{-x}\left(x^3-x^2+5 x-1\right)+C$

C

$e^{-x}\left(x^3+x^2+5 x+1\right)+C$

D

$-e^{-x}\left(x^3+x^2+5 x+1\right)+C$

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