Mathematics

# The value of $\int _{ 1/e }^{ \tan { x } }{ \dfrac { t }{ 1+{ t }^{ 2 } } dt+ } \int _{ 1/e }^{ \cot { x } }{ \dfrac { t }{ t\left( 1+{ t }^{ 2 } \right) } dt }$, where $x\in \left( \pi /6,\ \pi /3 \right)$, is equal to :

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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 Medium
Find: $\displaystyle \int{\dfrac{4}{(x-2)(x^{2}+4)}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \lim_{n \rightarrow \infty} \Sigma_{i=1}^n log \left(2 +\dfrac{5i}{n} \right) \dfrac{5}{n}$ is equal to?
• A. $\int_2^5 ln(x) dx$
• B. $\int_3^7 ln(x) dx$
• C. $\int_2^7 ln(x^2) dx$
• D. $\int_2^7 ln(x) dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle\int{\frac{x^2-1}{x^3\sqrt{2x^4-2x^2+1}}dx}$ is equal to
• A. $\displaystyle\frac{\sqrt{2x^4-2x^5+1}}{x^2}+C$
• B. $\displaystyle\frac{\sqrt{2x^4-2x^2+1}}{x^3}+C$
• C. $\displaystyle\frac{\sqrt{2x^4+2x^2+1}}{x}+C$
• D. $\displaystyle\frac{\sqrt{2x^4-2x^2+1}}{2x^2}+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int \frac{1}{x(x^n+1)}dx$.

Evaluate $\int \dfrac {1}{a^{x}b^{x}}dx$