Mathematics

# Integral of $f(x)=\sqrt{(1+x^{2})}$ with respect to $x^{3}$ is

$\dfrac{2}{3}\dfrac{(1+x^{2})^{3/2}}{x}+k$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle\int {\dfrac{{{\text{ln}}\left( {{\text{e}}{{\text{x}}^{\text{x}}}} \right)}}{{{\text{x}}{{\text{e}}^{\text{x}}}{{\left( {{\text{lnx}}} \right)}^{\text{2}}}}}} {\text{dx}}\;{\text{is}}$
• A. $\dfrac{{\text{1}}}{{{{\text{e}}^{\text{x}}}{\text{lnx}}}}{\text{ + c}}$
• B. $\dfrac{{{e^2}}}{{{{\text{e}}^{\text{x}}}{\text{lnx}}}}{\text{ + c}}$
• C. $- \dfrac{1}{{{{\text{e}}^{{\text{ - x}}}}{\text{lnx}}}}{\text{ + c}}$
• D. $- \dfrac{1}{{{{\text{e}}^{\text{x}}}{\text{lnx}}}}{\text{ + c}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium

$\displaystyle \int_{0}^{1}\frac{\sqrt{x}}{1+x}dx_{=}$
• A. $1-\pi/2$
• B. $\pi/2$
• C. $2+\pi/2$
• D. $2-\pi/2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate the given integral.
$\displaystyle \int { \tan ^{ -1 }{ \left( \cfrac { 2x }{ 1-{ x }^{ 2 } } \right) } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
$I = \int \sqrt{\frac{a+x}{a-x}}dx$

Evaluate: $\displaystyle \overset{\pi/2}{\underset{0}{\int}} \sin x\cdot \sin 2x \,\,dx$.