Mathematics

# $\displaystyle \int x.\frac{\ln \left ( x+\sqrt{1+x^2} \right )}{\sqrt{1+x^2}} dx$ equals

$\sqrt{1+x^2}\ln \left ( x+\sqrt{1+x^2} \right )-x+c$

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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 $\displaystyle\int^{\pi/2}_0\sin^2xdx$
• A. $\dfrac{\pi}{3}$
• B. $\dfrac{\pi}{2}$
• C. $\dfrac{2\pi}{3}$
• D. $\dfrac{\pi}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Evalaute the integral
$\displaystyle \int_{0}^{\pi}xf(\sin x)dx$
• A. $2\pi$
• B. $\displaystyle \pi\int_{0}^{\pi}f(\cos x)dx$
• C. $\displaystyle \pi\int_{0}^{\pi}f(\sin x) dx$
• D. $\displaystyle \pi\int_{0}^{\pi/2}f(\cos x)dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The integral of $f(x) = \dfrac{1}{x\ell n x}$ is
• A. $x \ell n x + c$
• B. $\dfrac{x}{\ell n x} + c$
• C. $x + \ell n x +$
• D. $\ell n(\ell n x) + c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the function    $x \sin 3x$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium

$\displaystyle \int_{0}^{a}\frac{x^{5}dx}{\sqrt{a^{2}-x^{2}}}=$
• A. $\displaystyle \frac{\mathrm{a}^{5}}{15}$
• B. $\displaystyle \frac{8a}{15}$
• C. $\displaystyle \frac{11\mathrm{a}^{2}}{15}$
• D. $\displaystyle \frac{8\mathrm{a}^{5}}{15}$