1
COMEDK 2024 Morning Shift
+1
-0

$$\int \sqrt{x^2-4 x+2} d x=$$

A
$$\frac{1}{2}(x-2) \sqrt{x^2-4 x+2}+\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C$$
B
$$(x-2) \sqrt{x^2-4 x+2}+\frac{1}{2} \log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C$$
C
$$\frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\sin ^{-1} \frac{x-2}{\sqrt{2}}+C$$
D
$$\frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C$$
2
COMEDK 2024 Morning Shift
+1
-0

$$\int \frac{x}{x^4-16} d x=$$

A
$$\frac{1}{16} \log \left|\frac{x^2+4}{x^2-4}\right|+C$$
B
$$\frac{1}{4} \log \left|\frac{x^2+4}{x^2-4}\right|+C$$
C
$$\frac{1}{16} \log \left|\frac{x^2-4}{x^2+4}\right|+C$$
D
$$\frac{1}{8} \log \left|\frac{x^2-4}{x^2+4}\right|+C$$
3
COMEDK 2024 Morning Shift
+1
-0

$$\text { The value of } \int \frac{1}{x+\sqrt{x-1}} d x \text { is }$$

A
$$\log (x+\sqrt{x-1})+\sin ^{-1}\left(\sqrt{\frac{x-1}{x}}\right)+C$$
B
$$\log (x+\sqrt{x-1})-\frac{2}{\sqrt{3}} \tan ^{-1}\left(\frac{2 \sqrt{x-1}+1}{\sqrt{3}}\right)+C$$
C
$$\log (x+\sqrt{x-1})+C$$
D
$$\log (x-1+\sqrt{x-1})+\frac{1}{\sqrt{3}} \log \left|\frac{x-2-\sqrt{3}}{x-2+\sqrt{3}}\right|+C$$
4
COMEDK 2023 Morning Shift
+1
-0

$$\int \frac{x d x}{2(1+x)^{3 / 2}}$$ is equal to

A
$$\frac{2+x}{\sqrt{1+x}}+C$$
B
$$\frac{2+x}{x \sqrt{1+x}}+C$$
C
$$\frac{x}{\sqrt{1+x}}+C$$
D
$$-\frac{x}{\sqrt{1+x}}+C$$
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