Mathematics

# Let $f\left( x \right) =\cfrac { 2\sin ^{ 2 }{ x } -1 }{ \cos { x } } +\cfrac { \cos { x } \left( 2\sin { x } +1 \right) }{ 1+\sin { x } }$ then $\int { { e }^{ x }\left( f\left( x \right) +f'\left( x \right) \right) dx }$ (where c is the constant of integration)

${ e }^{ x }\tan { x } +c$

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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
Evaluate $I = \displaystyle \int_{\pi /6}^{\pi /3}\sin x\:dx$
• A. $\displaystyle \frac{\sqrt{3}+1}{2}$
• B. $\displaystyle \frac{\sqrt{3}-1}{2\sqrt{3}}$
• C. None of these
• D. $\displaystyle \frac{1-\sqrt{3}}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
$\displaystyle \int { co\sec { x } \log { \left( co\sec { x } -\cot { x } \right) } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int\limits_{ - 4} {{e^{{{\left( {x + 5} \right)}^2}}}dx\, + 3} \,\,\,\int_{\frac{1}{3}}^{\frac{2}{3}} {{e^{9{{\left( {\frac{{x - 2}}{3}} \right)}^2}}}}$ is equal to
• A. $e^4$
• B. $3e^2$
• C. $0$
• D. $e^5$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate:
$\int { \cfrac { \sec ^{ 2 }{ x } \left( \log { x } \right) }{ x } } dx\quad$

$\displaystyle\int \left(e^x\right)^2 e^x dx$ is equal to