1
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
$$\log (x-1+\sqrt{x-1})+\frac{1}{\sqrt{3}} \log \left|\frac{x-2-\sqrt{3}}{x-2+\sqrt{3}}\right|+C$$
2
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
$$-\frac{x}{\sqrt{1+x}}+C$$
3
COMEDK 2023 Morning Shift
+1
-0

$$\int \frac{4^x}{\sqrt{1-16^x}} d x$$ is equal to

A
$$(\log 4) \sin ^{-1} 4^x+C$$
B
$$\frac{1}{4} \sin ^{-1}\left(4^x\right)+C$$
C
$$\frac{1}{\log 4} \sin ^{-1} 4^x+C$$
D
$$4 \log 4 \sin ^{-1} 4+C$$
4
COMEDK 2023 Evening Shift
+1
-0

$$\int x^x(1+\log x) d x$$ is equal to

A
$$x \log x+c$$
B
$$x^x+c$$
C
$$x^x \log x+c$$
D
$$x^{x-1}+c$$
EXAM MAP
Medical
NEET