Match List-I with List-II

List-I (Definite Integral)	List-II (Value)
(A) $\int_{1}^{2} e^x\,dx$	(I) $\frac{e^2(e^2-1)}{2}$
(B) $\int_{0}^{1} e^x\,dx$	(II) $\frac{(e^2-1)}{2}$
(C) $\int_{1}^{2} e^{2x}\,dx$	(III) $e-1$
(D) $\int_{0}^{1} e^{2x}\,dx$	(IV) $e(e-1)$

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Match List-I with List-II

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If $g(x) = \int \frac{dx}{x^{1/2} + x^{1/6}}$, then $g(1) - g(0)$ is :

Which of the following is/are correct?

A. $\int e^x\left[\frac{1}{(x-2)}-\frac{1}{(x-2)^2}\right]dx=\frac{e^x}{(x-2)}+C$, where C is an arbitrary constant.

B. $\int e^x\left[\frac{1}{(x-2)^3}-\frac{3}{(x-2)^4}\right]dx=\frac{e^x}{(x-2)^2}+C$, where C is an arbitrary constant.

C. $\int e^x\left[\frac{x-4}{(x-2)^3}\right]dx=\frac{e^x}{(x-2)^2}+C$, where C is an arbitrary constant.

D. $\int e^x\left[\frac{1}{x+2}-\frac{3}{(x+2)^2}\right]dx=\frac{e^x}{(x+2)^2}+C$, where C is an arbitrary constant.

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The value of $\displaystyle\int_0^1 xe^{x^2}\,dx$ is equal to :

$\int \frac{e^x(1 + x)dx}{\cos^2(e^x x)}$ is equal to

The value of the integral $I = \int_0^1 \frac{1}{\sqrt{1+3\sqrt{x}}} dx$ is