Mathematics

$\displaystyle \int _{0}^{\infty}\dfrac{dx}{(x+\sqrt{x^{2}+1})^{n}}\ (n\ \in \ N)(n\pm 1)$ is

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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

$\displaystyle \int e^{x}(\frac{\cos x-\sin x}{1-\cos 2x})dx=$
• A. $\dfrac{1}{2}e^{x}\cos ecx-x+c$
• B. $\dfrac{1}{2}e^{x}\sec x+c$
• C. $-\displaystyle \frac{1}{2}e^{x}\sec x+c$
• D. $-\displaystyle \frac{1}{2}e^{x}\cos ecx+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int\frac{x}{(1+x^{2})^{3/2}}dx=$
• A. $\displaystyle \frac{1}{(1+x^{2})}+c$
• B. $\displaystyle \frac{-1}{(1+x^{2})^{3/2}}+c$
• C. $\displaystyle \frac{-1}{(1+x^{2})}+c$
• D. $\displaystyle \dfrac{-1}{\sqrt{1+x^{2}}}+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate: $\int {\sqrt {\frac{{1 - x}}{{1 - x}}} } dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of $\displaystyle\int \dfrac {\sin 2x}{\sin^{4}x + \cos^{4}x} dx$ is
• A. $\tan^{-1} (\cot^{2}x) + C$
• B. $\tan^{-1} (\sin 2x) + C$
• C. $\tan^{-1} (\tan^{2} x) + C$
• D. $-\tan^{-1} (\cos 2x) + C$

$\displaystyle\int e^x\left(\dfrac{1}{x}-\dfrac{1}{x^2}\right)\ dx$.