Mathematics

# $\int \frac{1}{x(x^{n}-1)}dx$

$\frac{1}{n} log\left | \frac{x^{n}}{x^{n}+1} \right |+ c$

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate $\displaystyle \int \frac{1}{(x-1)(x^{2}+1)}dx$
• A. $\displaystyle \frac{1}{2}log(x-1)+\frac{1}{4}log(x^{2}+1)-\frac{1}{2}\tan ^{-1}x+c$
• B. $\displaystyle \frac{1}{2}log(x-1)-\frac{1}{2}log(x^{2}+1)-\frac{1}{2}\tan ^{-1}x+c$
• C. $\displaystyle \frac{1}{2}log(x-1)-\frac{1}{4}log(x^{2}+1)+\tan ^{-1}x+c$
• D. $\displaystyle \frac{1}{2}log(x-1)-\frac{1}{4}log(x^{2}+1)-\frac{1}{2}\tan ^{-1}x+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\int _{-1 }^{ 1 }\dfrac {{\sqrt {1+x+x^2}- \sqrt { 1-x+x^2 } } }{\sqrt { 1+x+x^2 }+\sqrt { 1-x+x^2} } dx=$
• A. $\dfrac {3\pi}{2}$
• B. $\dfrac {\pi}{2}$
• C. $-1$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int\frac{x}{(x^{2}-a^{2})(x^{2}-b^{2})}dx=$
• A. $\displaystyle \frac{1}{2(a^{2}-b^{2})}\log|\frac{x^{2}-b^{2}}{x^{2}-a^{2}}|+c$
• B. $\displaystyle \log|\frac{x^{2}-a^{2}}{x^{2}-b^{2}}|+c$
• C. $\displaystyle \frac{1}{(a^{2}-b^{2})}\log|\frac{x^{2}-a^{2}}{x^{2}-b^{2}}|+c$
• D. $\displaystyle \frac{1}{2(a^{2}-b^{2})}\log|\frac{x^{2}-a^{2}}{x^{2}-b^{2}}|+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the function    $\displaystyle \frac {3x^2}{x^6+1}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Let us consider the integral of the following forms
$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$
Case I If $m>0$, then put $\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$
Case II If $p>0$, then put $\sqrt{mx^2+nx+C}=u\pm \sqrt{p}$
Case III If quadratic equation $mx^2+nx+p=0$ has real roots $\alpha$ and $\beta$, then put $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$