1
MHT CET 2023 10th May Evening Shift
+2
-0

The value of $$\int \frac{\left(x^2-1\right) d x}{x^3 \sqrt{2 x^4-2 x^2+1}}$$ is

A
$$2 \sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$2 \sqrt{2+\frac{2}{x^2}+\frac{1}{x^4}}+c$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\frac{1}{2} \sqrt{2-\frac{2}{x^2}+\frac{1}{x^4}}+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$2 \sqrt{2-\frac{2}{x^2}-\frac{1}{x^4}}+c$$, where $$\mathrm{c}$$ is a constant of integration.
2
MHT CET 2023 10th May Evening Shift
+2
-0

$$\int \mathrm{e}^x\left(1-\cot x+\cot ^2 x\right) \mathrm{d} x=$$

A
$$\mathrm{e}^x \cdot \cot x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\mathrm{e}^x \cdot \operatorname{cosec} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$-\mathrm{e}^x \cdot \cot x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$-\mathrm{e}^x \cdot \operatorname{cosec} x+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
3
MHT CET 2023 10th May Morning Shift
+2
-0

If $$\int \sqrt{\frac{x-7}{x-9}} d x=A \sqrt{x^2-16 x+63}+\log \left|(x-8)+\sqrt{x^2-16 x+63}\right|+c,$$

(where $$\mathrm{c}$$ is a constant of integration) then $$\mathrm{A}$$ is

A
$$-1$$
B
$$\frac{1}{2}$$
C
$$1$$
D
$$\frac{-1}{2}$$
4
MHT CET 2023 10th May Morning Shift
+2
-0

$$\int \frac{1}{7-6 x-x^2} d x=$$

A
$$\frac{1}{4} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
B
$$\frac{1}{8} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
C
$$\frac{1}{16} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
D
$$\frac{1}{32} \log \left(\frac{7+x}{1-x}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant of integration.
EXAM MAP
Medical
NEET