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1
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{2}{1+x+x^2} d x= $$
A
$\frac{4}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c$
B
$\frac{4}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$
C
$\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x-1}{\sqrt{3}}\right)+c$
D
$\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+c$
2
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{1}{x^2\left(\sqrt{1+x^2}\right)} d x= $$

A
$\frac{-\sqrt{x^2+1}}{x}+c$
B
$\frac{\sqrt{x^2+1}}{x}+c$
C
$\frac{-\sqrt{x^2-1}}{x}+c$
D
$\frac{\sqrt{x^2-1}}{x}+c$
3
AP EAPCET 2024 - 22th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int \frac{\sin 7 x}{\sin 2 x \sin 5 x} d x= $$

A
$\log (\sin 5 x \sin 2 x)+c$
B
$\log (\sin 5 x)+\log (\sin 2 x)+c$
C
$\frac{1}{5} \log (\sin 5 x)+\frac{1}{2} \log (\sin 2 x)+c$
D
$\frac{1}{5} \log (\sin x)+\frac{1}{2} \log (\sin x)+c$
4
AP EAPCET 2024 - 21th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $\frac{x+2}{\left(x^2+3\right)\left(x^4+x^2\right)\left(x^2+2\right)}=\frac{A x+B}{x^2+3}+\frac{C x+D}{x^2+2}$ $+\frac{E x^3+F x^2+G x+H}{x^4+x^2}$, then $(E+F)(C+D)(A)=$
A
$-\frac{1}{4}$
B
$-\frac{3}{4}$
C
$\frac{3}{4}$
D
$\frac{1}{4}$
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