Mathematics

The value of $\int {\frac{{(1 + {x^2})dx}}{{(1 - {x^2})\sqrt {1 + {x^2} + {x^4}} }}}$,is

$- \frac{1}{{2\sqrt 3 }}{\rm{log}}\left| {\frac{{\sqrt {{x^4} + {x^2} + 1} - \sqrt {3x} }}{{\sqrt {{x^4} + {x^2} + 1} + \sqrt {3x} }}} \right| + C$

$\frac{1}{{2\sqrt 3 }}{\rm{log}}\left| {\frac{{\sqrt {{x^4} + {x^2} + 1} + \sqrt {2x} }}{{\sqrt {{x^4} + {x^2} + 1} - \sqrt {2x} }}} \right| + C$

$\frac{1}{{2\sqrt 3 }}{\rm{log}}\left| {\frac{{\sqrt {{x^4} - {x^2} + 1} - \sqrt {3x} }}{{\sqrt {{x^4} + {x^2} + 1} + \sqrt {3x} }}} \right| + C$

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Multiple Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

Realted Questions

Q1 Single Correct Medium
If $\displaystyle I=\int { \left( \sqrt { \tan { x } } +\sqrt { \cot { x } } \right) } dx=f\left( x \right)+c$
• A. $\sqrt { 2 } \sin ^{ 1 }\times \left( \sin { x } -\cos { x } \right)$
• B. $\sqrt { 2 } \sin ^{ 1- }\times \left( \sin { x } +\cos { x } \right)$
• C. $none\ of these$
• D. $\sqrt { 2 } \sin ^{ -1 }\times \left( \sin { x } -\cos { x } \right)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\int { \dfrac { arc\sin { \sqrt { x } } }{ \sqrt { 1-x } } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle \int_{1}^{2} e^{x^2} dx= a$, then $\displaystyle \int_{e}^{e^4}\sqrt{\ln x} \:dx$ is equal to
• A. $2e^4-2e-a$
• B. $2e^4-e-2a$
• C. $e^4-e-a$
• D. $2e^4-e-a$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int { \dfrac { dx }{ 16{ x }^{ 2 }-25 } }$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$