# Indefinite Integrals · Mathematics · WB JEE

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## Subjective

WB JEE 2008
Evaluate $$\int {{{{x^2}} \over {x(1 + {x^2})}}dx}$$

WB JEE 2009
$$\int {{{dx} \over {x(x + 1)}}}$$ equals where c is arbitrary constant.
WB JEE 2009
The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ..... + {n \over {{n^2} + {n^2}}... WB JEE 2009 The value of$$\int\limits_{ - 1}^1 {{{|x + 2|} \over {x + 2}}dx} $$is WB JEE 2009$$\int {{{dx} \over {\sin x + \sqrt 3 \cos x}}} $$equals WB JEE 2009$$\int {{{{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx} $$equal to where c is an arbitrary constant WB JEE 2010$$\int {{{\log \sqrt x } \over {3x}}dx} $$is equal to WB JEE 2010$$\int {{e^x}\left( {{2 \over x} - {2 \over {{x^2}}}} \right)dx} $$is equal to WB JEE 2010 The value of the integral$$\int {{{dx} \over {{{({e^x} + {e^{ - x}})}^2}}}} $$is WB JEE 2010$$\int {\sqrt {1 + \cos x} dx} $$is equal to WB JEE 2011$$\int {{{{x^3}dx} \over {1 + {x^8}}} = } $$WB JEE 2011$$\int {{{\cos 2x} \over {\cos x}}dx = } $$WB JEE 2011$$\int {{{{{\sin }^8}x - {{\cos }^8}x} \over {1 - 2{{\sin }^2}x{{\cos }^2}x}}dx} $$WB JEE 2011$$\int {{2^x}(f'(x) + f(x)\log 2)dx} $$is WB JEE 2023 If$$I = \int {{{{x^2}dx} \over {{{(x\sin x + \cos x)}^2}}} = f(x) + \tan x + c} $$, then$$f(x)$$is WB JEE 2023 If$$\int {{{dx} \over {(x + 1)(x - 2)(x - 3)}} = {1 \over k}{{\log }_e}\left\{ {{{|x - 3{|^3}|x + 1|} \over {{{(x - 2)}^4}}}} \right\} + c} $$, then ... WB JEE 2022$$I = \int {\cos (\ln x)dx} $$. Then I = WB JEE 2022 Let$$\int {{{{x^{{1 \over 2}}}} \over {\sqrt {1 - {x^3}} }}dx = {2 \over 3}g(f(x)) + c} $$; then (c denotes constant of integration) WB JEE 2021 If$$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }_e}\left| {a + b\cos x} \right| + {a \over {a + b\cos x}}} \right] + c...
WB JEE 2020
$$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\phi (x) - 1} }}dx = }$$
WB JEE 2019
If $$\int {\cos x\log \left( {\tan {x \over 2}} \right)} dx$$ = $$\sin x\log \left( {\tan {x \over 2}} \right)$$ + f(x), then f(x) is equal to (assumi...
WB JEE 2019
y = $$\int {\cos \left\{ {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right\}} dx$$ is an equation of a family of
WB JEE 2019
If $$\int {{2^{{2^x}}}.\,{2^x}dx} = A\,.\,{2^{{2^x}}} + C$$, then A is equal to
WB JEE 2018
If $$\int {{e^{\sin x}}} .\left[ {{{x{{\cos }^3}x - \sin x} \over {{{\cos }^2}x}}} \right]dx = {e^{\sin x}}f(x) + c$$, where c is constant of integrat...
WB JEE 2018
If $$\int {f(x)} \sin x\cos xdx = {1 \over {2({b^2} - {a^2})}}\log (f(x)) + c$$, where c is the constant of integration, then f(x) is equal to
WB JEE 2017
$$\int {\cos (\log x)dx}$$ = F(x) + C, where C is an arbitrary constant. Here, F(x) is equal to
WB JEE 2017
$$\int {{{{x^2} - 1} \over {{x^4} + 3{x^2} + 1}}dx}$$ (x > 0) is
WB JEE 2017
Let I = $$\left| {\int {_{10}^{19}{{\sin x} \over {1 + {x^8}}}dx} } \right|$$. Then,
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