Mathematics

# Evaluate$\int \dfrac {x+2}{2X^{2}+6x+5}dx$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 TRUE/FALSE Medium
$\int \sqrt {x^2 + a^2} dx =\dfrac{x}{2} \sqrt {x^2 + a^2} + \dfrac{a^2}{2} log (x +\sqrt {x^2 + a^2)} +c$
• A. False
• B. True

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle\int{\frac{(1+x^2)dx}{(1-x^2)\sqrt{1+x^2+x^4}}} =$
• A. $\displaystyle I=-\frac{1}{2\sqrt{3}}\log{\left|\frac{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}-\sqrt{5}}{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}+\sqrt{5}}\right|}+C$
• B. $\displaystyle I=-\frac{1}{4\sqrt{3}}\log{\left|\frac{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}-\sqrt{3}}{\sqrt{2x^2+\displaystyle\frac{1}{x^2}+1}+\sqrt{3}}\right|}+C$
• C. $\displaystyle I=-\frac{1}{2\sqrt{3}}\log{\left|\frac{\sqrt{2x^2+\displaystyle\frac{1}{2x^2}+1}-\sqrt{3}}{\sqrt{2x^2+\displaystyle\frac{1}{2x^2}+1}+\sqrt{3}}\right|}+C$
• D. $\displaystyle I=-\frac{1}{2\sqrt{3}}\log{\left|\frac{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}-\sqrt{3}}{\sqrt{x^2+\displaystyle\frac{1}{x^2}+1}+\sqrt{3}}\right|}+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the given integral.
$\displaystyle \int { { e }^{ x } } \left( \tan ^{ -1 }{ x } +\cfrac { 1 }{ 1+{ x }^{ 2 } } \right) dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:
$\int { \dfrac { dx }{ 2{ x }^{ 2 }+x-1 } }$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$