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1
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

$$ \int e^{4 x}(\sin 3 x-\cos 3 x) d x= $$

A

$\frac{e^{4 x}}{25}(7 \sin 3 x-\cos 3 x)+C$

B

$\frac{e^{4 x}}{25}(\sin 3 x-7 \cos 3 x)+C$

C

$\frac{e^{4 x}}{5}(7 \sin 3 x+\cos 3 x)+C$

D

$\frac{e^{4 x}}{5}(\sin 3 x+7 \cos 3 x)+C$

2
TG EAPCET 2025 (Online) 2nd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

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

A

$\frac{1}{1+(\log x)^2}+C$

B

$\frac{\log x}{1+(\log x)^2}+C$

C

$\frac{x}{1+(\log x)^2}+C$

D

$\frac{x^2}{1+(\log x)^2}+C$

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

If $\int(x+2) \sqrt{x^2-x+2} d x=\frac{1}{3} f(x)+\frac{5}{8} g(x)+\frac{35}{16} h(x)+C$ then $f(-1)+g(-1)+h\left(\frac{1}{2}\right)=$

A

-4

B

$2+\ln \left(\frac{\sqrt{7}}{2}\right)$

C

4

D

-2

4
TG EAPCET 2024 (Online) 11th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\sec x}{3(\sec x+\tan x)+2} d x=$
A
$\frac{1}{2} \log \left|\frac{\tan \frac{x}{2}+1}{\tan \frac{x}{2}+5}\right|+C$
B
$\frac{2}{\sqrt{11}} \tan ^{-1}\left\{\frac{3 \tan \frac{x}{2}+4}{\sqrt{11}}\right\}+C$
C
$\log |3 \sec x+2 \tan x|+C$
D
$\log |3 \tan x+2 \sec x|+C$.
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