Mathematics

# Evaluate $\displaystyle\int \dfrac {e^{x}(1+x)}{\sin^{2}(xe^{x})}dx$

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

#### Realted Questions

Q1 Single Correct Medium
The value of $\int \sqrt{\dfrac{1 - \sqrt{2}}{1 + \sqrt{x}}} dx$ is equal to :
• A. $-2 \sqrt{1 - x} + cos^{-1} \, \sqrt{x} + \sqrt{x (1 - x)} + c$
• B. $-2 \sqrt{1 + x} + cos^{-1} \, \sqrt{x} + \sqrt{x (1 - x)} + c$
• C. none of these
• D. $-2 \sqrt{1 - x} + cos^{-1} \, \sqrt{x} + \sqrt{1 - x + c}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int_{0}^{\infty} \dfrac {x \ln x}{(1 + x^{2})^{2}}dx =$
• A. $1$
• B. $-1$
• C. $\dfrac {\pi}{2}$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate : $\int \dfrac { 1 } { ( x + 1 ) \sqrt { 3 + 2 x - x } } d x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of $\smallint {\textstyle{1 \over {x + \sqrt {x - 1} }}}$ dx is
• A. $\log \left( {x + \sqrt {x - 1} } \right) + {\sin ^{ - 1}}\sqrt {\frac{{x - 1}}{x}} + C$
• B. $\log \left( {x + \sqrt {x - 1} } \right) + C$
• C. none of these
• D. $\log \left( {x + \sqrt {x - 1} } \right) - \frac{2}{3}{\tan ^{ - 1}}\left\{ {\frac{{2\sqrt {x - 1} + 1}}{{\sqrt 3 }}} \right\}C$

$\displaystyle\int^0_{-2}(x^3+3x^2+3x+(x+1)\cos(x+1)dx$.