1
WB JEE 2009
+1
-0.25

$$\int {{{dx} \over {x(x + 1)}}}$$ equals

where c is arbitrary constant.

A
$$\ln \left| {{{x + 1} \over x}} \right| + c$$
B
$$\ln \left| {{x \over {x + 1}}} \right| + c$$
C
$$\ln \left| {{{x - 1} \over x}} \right| + c$$
D
$$\ln \left| {{{x - 1} \over {x + 1}}} \right| + c$$
2
WB JEE 2009
+1
-0.25

The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ..... + {n \over {{n^2} + {n^2}}}} \right]$$ is

A
$$\pi$$ / 4
B
log 2
C
0
D
1
3
WB JEE 2009
+1
-0.25

The value of $$\int\limits_{ - 1}^1 {{{|x + 2|} \over {x + 2}}dx}$$ is

A
1
B
2
C
0
D
$$-$$1
4
WB JEE 2009
+1
-0.25

$$\int {{{dx} \over {\sin x + \sqrt 3 \cos x}}}$$ equals

A
$${1 \over 2}\ln \left| {\tan \left( {{x \over 2} - {\pi \over 6}} \right)} \right| + c$$
B
$${1 \over 2}\ln \left| {\tan \left( {{x \over 4} - {\pi \over 6}} \right)} \right| + c$$
C
$${1 \over 2}\ln \left| {\tan \left( {{x \over 2} + {\pi \over 6}} \right)} \right| + c$$
D
$${1 \over 2}\ln \left| {\tan \left( {{x \over 4} + {\pi \over 6}} \right)} \right| + c$$
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