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1
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\cos x+x \sin x}{x(x+\cos x)} d x=$
A
$\log \left|x^2+x \cos x\right|+c$
B
$\log \left|\frac{x}{x+\cos x}\right|+c$
C
$\log \left|\frac{\cos x}{x+\cos x}\right|+c$
D
$\log \left|\frac{1}{x+\cos x}\right|-\log x+c$
2
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int \sqrt{\frac{2}{1+\sin x}} d x=2 \log |A(x)-B(x)|+C$ and $0 \leq x \leq \frac{\pi}{2}$, then $B\left(\frac{\pi}{4}\right)=$
A
$\frac{1}{\sqrt{2+3 \sqrt{3}}}$
B
$\frac{1}{\sqrt{3+2 \sqrt{2}}}$
C
$\frac{-1}{\sqrt{3+2 \sqrt{2}}}$
D
$\frac{2}{\sqrt{2+\sqrt{2}}}$
3
AP EAPCET 2024 - 20th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \begin{aligned} &\text { If } \int \frac{3}{2 \cos ^3 x \sqrt{2 \sin 2 x}} d x=\frac{3}{2}(\tan x)^B+\frac{3}{10}(\tan x)^A+C \text {, than }\\&A= \end{aligned} $$

A
$\frac{1}{2}$
B
1
C
5
D
$\frac{5}{2}$
4
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1}$, then $B D-A C=$
A
$\frac{3}{8}$
B
$\frac{1}{8}$
C
1
D
0
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