1
COMEDK 2024 Evening Shift
+1
-0

$$\int e^x\left[\frac{x^2+1}{(x+1)^2}\right] d x \quad \text { is equal to }$$

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

If $$\int \frac{1}{\sqrt{\sin ^3 x \cos x}} d x=\frac{k}{\sqrt{\tan x}}+c$$ then the value of $$k$$ is

A
$$-2$$
B
1
C
2
D
$$-1$$
3
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
$$\frac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C$$
4
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
$$\frac{1}{8} \log \left|\frac{x^2-4}{x^2+4}\right|+C$$
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