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1
KCET 2025
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\mathrm{dx}}{\mathrm{x}^2\left(\mathrm{x}^4+1\right)^{3 / 4}}$ equals
A
$\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+c$
B
$\left(x^4+1\right)^{\frac{1}{4}}+c$
C
$-\left(\mathrm{x}^4+1\right)^{\frac{1}{4}}+\mathrm{c}$
D
$-\left(\frac{x^4+1}{x^4}\right)^{\frac{1}{4}}+c$
2
KCET 2024
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{\sin x}{3+4 \cos ^2 x} d x$$

A
$-\frac{1}{2 \sqrt{3}} \tan ^{-1}\left(\frac{2 \cos x}{\sqrt{3}}\right)+C$
B
$\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{\cos x}{3}\right)+C$
C
$\frac{1}{2 \sqrt{3}} \tan ^{-1}\left(\frac{\cos x}{3}\right)+C$
D
$-\frac{1}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \cos x}{3}\right)+C$
3
KCET 2024
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1}{x\left[6(\log x)^2+7 \log x+2\right]} d x \text { is }$$

A
$\frac{1}{2} \log \left|\frac{2 \log x+1}{3 \log x+2}\right|+C$
B
$\log \left|\frac{2 \log x+1}{3 \log x+2}\right|+c$
C
$\log \left|\frac{3 \log x+2}{2 \log x+1}\right|+C$
D
$\frac{1}{2} \log \left|\frac{3 \log x+2}{2 \log x+1}\right|+C$
4
KCET 2024
MCQ (Single Correct Answer)
+1
-0

$\int \frac{\sin \frac{3 x}{2}}{\sin \frac{x}{2}} d x$ is

A
$2 x+\sin x+2 \sin 2 x+C$
B
$x+2 \sin x+2 \sin 2 x+C$
C
$x+2 \sin x+\sin 2 x+C$
D
$2 x+\sin x+\sin 2 x+C$
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