Mathematics

# Find the value of the equation  $\int _ { 0 } ^ { \infty } \dfrac { d x } { \left( x + \sqrt { x ^ { 2 } + 1 } \right) ^ { 3 } } =?$

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

#### Realted Questions

Q1 Single Correct Medium

Find $\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{\sec^{2}xdx}{(\sec x+\tan x)^{n}}$, where $(\mathrm{n}>2)$
• A. $\displaystyle \frac{1}{n^{2}-1}$
• B. $\displaystyle \frac{n}{n^{2}+1}$
• C. $\displaystyle \frac{2}{n^{2}-1}$
• D. $\displaystyle \frac{n}{n^{2}-1}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate:  $\dfrac{dy}{dx}=\left( { x }^{ 3 }+x+1 \right)$ w.r.t $x$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int e^{x}(\dfrac{1+\sqrt{1-x^{2}}\sin^{-1}x}{\sqrt{1-x^{2}}}) dx =$
• A. $\displaystyle \dfrac{e^{x}}{\sqrt{1-x^{2}}}+c$
• B. $e^{x}(e^{sin^{-1}x}+\displaystyle \dfrac{1}{\sqrt{1-x^{2}}})+c$
• C. ${e^{sin^{-1}x}}+\displaystyle \dfrac{1}{\sqrt{1-x^{2}}}+c$
• D. $e^{x}\sin^{-1}x+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle\int \cos \left[2\cot^{-1}\sqrt{\dfrac{1-x}{1+x}}\right]dx$ is equal to?
• A. $\dfrac{1}{2}\sin \left[2\cot^{-1}\sqrt{\dfrac{1-x}{1+x}}\right]+c$
• B. $-\dfrac{1}{2}x^2+c$
• C. $\dfrac{1}{2}x+c$
• D. $\dfrac{1}{2}x^2+c$

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 $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$