Mathematics

# Evaluate:$\displaystyle\int{\dfrac{dx}{{x}^{2}{\left({x}^{4}+1\right)}^{\frac{3}{4}}}}$

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int\frac{dx}{x\sqrt{1-x^{3}}}=$
• A. $\dfrac{1}{3}\log|\displaystyle \frac{\sqrt{1-x^{2}}+1}{\sqrt{1-x^{2}}-1}|+c$
• B. $\dfrac{1}{3}\log|\displaystyle \frac{1}{\sqrt{1-x^{3}}}|+c$
• C. $\displaystyle \frac{1}{3}\log|1-x^{3}|+c$
• D. $\dfrac{1}{3}\log|\displaystyle \frac{\sqrt{1-x^{3}}-1}{\sqrt{1-x^{3}}+1}|+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \frac{x^{2}}{(x^{2}+a^{2})(x^{2}+b^{2})}=k \left [\displaystyle \frac{a^{2}}{x^{2}+a^{2}}-\displaystyle \frac{b^{2}}{x^{2}+b^{2}} \right]\Rightarrow k=$
• A. $1$
• B. $\displaystyle \frac{1}{a^{2}+b^{2}}$
• C. $\displaystyle \frac{1}{b^{2}-a^{2}}$
• D. $\displaystyle \frac{1}{a^{2}-b^{2}}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Integrate :$\displaystyle\int{{\left({\left(\dfrac{x+1}{x-1}\right)}^{2}+{\left(\dfrac{x-1}{x+1}\right)}^{2}-2\right)}^{\frac{1}{2}}dx}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Antiderivation of $\dfrac {\sin^{2}x}{1+\sin^{2}x}$ w.r.t is:
• A. $x-\dfrac {2}{\sqrt {2}}arc\tan(\sqrt {2}\tan x)+C$
• B. $x+\sqrt {2} arc\tan(\sqrt {2}\tan x)+C$
• C. $x-\sqrt {2} arc\tan(\sqrt {2}\tan x)+C$
• D. $x-\dfrac {\sqrt {2}}{2} arc\tan(\sqrt {2}\tan x)+C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int\limits_{ - 5}^5 {\log \left( {\frac{{130 - {x^3}}}{{130 + {x^3}}}} \right)} dx$ is equal to
• A. $\log \frac{{57}}{5}$
• B. $2\int\limits_{ - 5}^5 {\log \left( {\frac{{130 - {x^3}}}{{130 + {x^3}}}} \right)} dx$
• C. $-1$
• D. $0$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020