1
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int(\sqrt{\tan x}+\sqrt{\cot x}) d x= $$

A

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

B

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

C

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

D

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

2
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$\int \frac{\sqrt{x-2}}{2 x+4} d x=$

A

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

B

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

C

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

D

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

3
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\int x^{49}\left[\tan ^{-1} x^{50}+\frac{x^{50}}{1+x^{100}}\right] d x=\frac{x^n}{k} f(x)+c$, then

$$ f(x)-f\left(\sqrt[k]{x^n}\right)= $$

A

$k+n$

B

$k-n$

C

$1 / k$

D

$1 / n$

4
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{x}{\sqrt{x^2-2 x+5}} d x= $$

A

$\sqrt{x^2-2 x+5}+\sinh ^{-1}\left(\frac{x-1}{2}\right)+C$

B

$\frac{1}{2} \sqrt{x^2-2 x+5}+\sin ^{-1}\left(\frac{x-1}{2}\right)+C$

C

$2 \sqrt{x^2-2 x+5}+\cosh ^{-1}\left(\frac{x-1}{2}\right)+C$

D

$\sqrt{x^2-2 x+5}-\cos ^{-1}\left(\frac{x-1}{2}\right)+C$