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1
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
Let $f(x)=\int \frac{x}{\left(x^2+1\right)\left(x^2+3\right)} d x$. If $f(3)=\frac{1}{4} \log \left(\frac{5}{6}\right)$, then $f(0)=$
A
$\frac{1}{4} \log \left(\frac{1}{3}\right)$
B
0
C
$\frac{1}{2} \log \left(\frac{1}{3}\right)$
D
$\log \left(\frac{1}{3}\right)$
2
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{2 \cos 2 x}{(1+\sin 2 x)(1+\cos 2 x)} d x= $$
A
$2 \tan x+\log (1+\tan x)+c$
B
$\tan x-2 \log (1+\tan x)+c$
C
$2 \log (1+\tan x)+\tan x+c$
D
$2 \log (1+\tan x)-\tan x+c$
3
AP EAPCET 2024 - 19th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int\left(\frac{x}{x \cos x-\sin x}\right)^2 d x= $$
A
$\frac{x \operatorname{cosec} x}{x \cos x-\sin x}+\cot x+c$
B
$\frac{x \operatorname{cosec} x}{x \cos x-\sin x}-\cot x+c$
C
$\frac{x \operatorname{cosec} x}{x \cos +\sin x}+\cot x+c$
D
$\frac{x}{x \cos x-\sin x}-\cot x+c$
4
AP EAPCET 2024 - 18th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{x^5 \sqrt[3]{x^3+1}} d x=$
A
$\frac{4}{\sqrt{x^5+1}}+c$
B
$4 x^4\left(x^5+1\right)^{4 / 3}+0$
C
$=\frac{\left(x^3+1\right)^{4 / 3}}{4 x^4}+c$
D
$-\frac{\left(x^5+1\right)^{45}}{4 x^5}+c$
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