Mathematics

# Solve $\displaystyle\int \dfrac{e^{x}+1}{e^{x}+x}dx$

$\log (e^x+x)+C$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Multiple Correct Hard
Let $\displaystyle u = \overset{\infty}{\underset{0}{\int}} \dfrac{dx}{x^4 + 7x^2 + 1} \& v = \overset{\infty}{\underset{0}{\int}} \dfrac{x^2 dx}{x^4 + 7x^2 + 1}$ then:
• A. v > u
• B. 6v = $\displaystyle \pi$
• C. $\displaystyle 3u+2v=5\pi /6$
• D. $\displaystyle u+v=\pi /3$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate
$\displaystyle \int{\dfrac{x^{2}\sin^{-1}x}{(1-x^{2})^{3/2}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate: $\int _{ 1/3 }^{ 1 }{ \cfrac { { \left( x-{ x }^{ 3 } \right) }^{ 1/3 } }{ { x }^{ 4 } } } dx=$
• A. $3$
• B. $0$
• C. $4$
• D. $6$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int_{0}^{\pi /2}\dfrac {1}{4\cos^{2}x+9\sin^{2}x}dx=$
• A. $\pi /10$
• B. $\pi /5$
• C. $\pi /2$
• D. $\pi /12$

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.