Mathematics

# $\displaystyle \int_{1}^{e} \dfrac {e^{x}}{x}(1+x\log x)dx=$

$e^{e}$

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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

Evaluate the following definite integral:

$\displaystyle\int_{0}^{\pi/2}\dfrac{\sin^{3/2} x}{\sin^{3/2}x+\cos^{3/2} x}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Solve : $\int \sin^{2} (2x+1) dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate : $\int \frac{dx}{a+be^{cx}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of definite integral $\displaystyle \int _{ 0 }^{ 1/3 }{ \dfrac { ln\left( 1+3x \right) }{ 1+{ 9x }^{ 2 } } } dx$ equals
• A. $\dfrac { \pi }{ 12 } \ell n2$
• B. $\dfrac { \pi }{ 16 } \ell n2$
• C. $\dfrac { \pi }{ 24 } \ell n2$
• D. $\dfrac { \pi }{ 8 } \ell n2$

Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.