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1
KCET 2019
MCQ (Single Correct Answer)
+1
-0

$$\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=$$

A
$$\tan ^{-1} \sqrt{x}+C$$
B
$$2 \log (\sqrt{x}+1)+C$$
C
$$2 \tan ^{-1} \sqrt{x}+C$$
D
$$\frac{1}{2} \tan ^{-1} \sqrt{x}+C$$
2
KCET 2019
MCQ (Single Correct Answer)
+1
-0

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{aligned}$$

Then $$A, B, C$$ are respectively

A
$$\frac{1}{6}, \frac{-1}{3}, \frac{1}{3}$$
B
$$\frac{-1}{6}, \frac{1}{3}, \frac{1}{3}$$
C
$$\frac{-1}{6}, \frac{-1}{3}, \frac{1}{2}$$
D
$$\frac{1}{6}, \frac{1}{3}, \frac{1}{5}$$
3
KCET 2018
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{1+e^x} d x$ is equal to
A
$\log _e\left(\frac{e^x+1}{e^x}\right)+C$
B
$\log _e\left(\frac{e^x-1}{e^x}\right)+C$
C
$\log _e\left(\frac{e^x}{e^x+1}\right)+C$
D
$\log _e\left(\frac{e^x}{e^x-1}\right)+C$
4
KCET 2018
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{\sqrt{3-6 x-9 x^2}} d x$ is equal to
A
$\sin ^{-1}\left(\frac{3 x+1}{2}\right)+C$
B
$\sin ^{-1}\left(\frac{3 x+1}{6}\right)+c$
C
$\frac{1}{3} \sin ^{-1}\left(\frac{3 x+1}{2}\right)+C$
D
$\sin ^{-1}\left(\frac{2 x+1}{3}\right)+C$
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