1
KCET 2023
+1
-0

$$\int \sqrt{5-2 x+x^2} d x$$ is equals to

A
\begin{aligned} \frac{x}{2} \sqrt{5-2 x+x^2} & +4 \log \mid(x+1)+\sqrt{x^2-2 x+5} \mid+C\end{aligned}
B
$$\frac{x-1}{2} \sqrt{5+2 x+x^2}+2 \log \mid(x-1)+\sqrt{5+2 x+x^2} \mid+C$$
C
$$\frac{x-1}{2} \sqrt{5-2 x+x^2}+2 \log \mid(x-1)+\sqrt{5-2 x+x^2} \mid+C$$
D
$$\frac{x-1}{2} \sqrt{5-2 x+x^2}+2 \log \mid(x+1)+\sqrt{x^2+2 x+5}|+C$$
2
KCET 2023
+1
-0

$$\int \frac{1}{1+3 \sin ^2 x+8 \cos ^2 x} d x$$ is equals to

A
$$\tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C$$
B
$$\frac{1}{6} \tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C$$
C
$$6 \tan ^{-1}\left(\frac{2 \tan x}{3}\right)+C$$
D
$$\frac{1}{6} \tan ^{-1}(2 \tan x)+C$$
3
KCET 2022
+1
-0

$$\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x$$ is equal to

A
$$2(\sin x-x \cos \alpha)+c$$
B
$$2(\sin x+x \cos \alpha)+c$$
C
$$2(\sin x-2 x \cos \alpha)+c$$
D
$$2(\sin x+2 x \cos \alpha)+c$$
4
KCET 2022
+1
-0

If $$\int \frac{d x}{(x+2)\left(x^2+1\right)}=a \log \left|1+x^2\right|+b \tan ^{-1} x +\frac{1}{5} \log |x+2|+c,$$ then

A
$$a=\frac{-1}{10}, b=\frac{2}{5}$$
B
$$a=\frac{1}{10}, b=\frac{2}{5}$$
C
$$a=\frac{-1}{10}, b=\frac{-2}{5}$$
D
$$a=\frac{1}{10}, b=\frac{-2}{5}$$
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