Mathematics

# $\int_{lnx-ln^{2}}^{ln\pi }\frac{e^{x}}{1-cos(\frac{2}{3}e^{e})}dx$ is equal to

$\frac{1}{\sqrt{3}}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Hard
Evaluate:
$\int { \cfrac { \sec ^{ 2 }{ x } \left( \log { x } \right) }{ x } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve:-
$\int \dfrac{{\cos \,x}}{{1 + \cos \,x}}d x$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int \frac{x^{3}dx}{\sqrt{1+x^{2}}}$ is equal to
• A. $\displaystyle \frac{1}{3}\sqrt{1+x^{2}}(2+x^{2})+C$
• B. $\displaystyle \frac{1}{3}\sqrt{1+x^{2}}(x^{2}-1)+C$
• C. $\displaystyle \frac{1}{3}(x^{2}-1)^{3/2}+C$
• D. $\displaystyle \frac{1}{3}\sqrt{1+x^{2}}(x^{2}-2)+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int\frac{\cos x}{(1+\sin x)(2+\sin x)}dx=$
• A. $\displaystyle \log|\frac{2+\sin x}{1+\sin x}|+c$
• B. $\log|(1+sinx)(2+\sin x)|+c$
• C. $\log|(1+sinx)+(2+\sin x)|+c$
• D. $\displaystyle \log|\frac{1+\sin x}{2+\sin x}|+c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int_{0}^{1} \tan^{-1}\left( \dfrac { 2x-1 }{ 1+x-{ x }^{ 2 } } \right) dx=$
• A. $1$
• B. $\pi$
• C. $2\pi$
• D. $0$