Mathematics

# The integral $\displaystyle\int { \dfrac { x+2 }{ \left( { x }^{ 2 }+3x+3 \right) \sqrt { x+1 } } } dx$ is equal to

$\dfrac { 1 }{ \sqrt { 3 } } \tan ^{ -1 }{ \left[ -\dfrac { x }{ \sqrt { 3\left( x+1 \right) } } \right] } +C$

Its FREE, you're just one step away

Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle \lim_{n\to \infty} \left[ \frac{n^{1/2}}{n^{3/2}} +\frac{n^{1/2}}{(n+3)^{3/2}}+\frac{n^{1/2}}{(n+6)^{3/2}}+......\frac{n^{1/2}}{ \left \{n+3(n-1)\right \}^{3/2} } \right]=$
• A. $1/5$
• B. $1/10$
• C. $1/2$
• D. $1/3$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $f(x)=\begin{vmatrix}\sin x+\sin2x+\sin3x & \sin2x & \sin3x\\ 3+4\sin x & 3 & 4\sin x\\ 1+\sin x & \sin x & 1\end{vmatrix}$, then the value of $\displaystyle \int_{0}^{\frac{\pi}2}f(x)dx$, is
• A. $3$
• B. $\dfrac23$
• C. $0$
• D. $\dfrac13$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integrals:$\displaystyle \int {\dfrac{x}{x+2}.dx}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int\dfrac{dx}{\sqrt{2ax^3}}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \overset{\pi/2}{\underset{0}{\int}}{ \dfrac { \sin ^6x }{ \cos ^{ 6 }{ x } +\sin ^{ 6 }{ x } } }dx$ is equal to:
• A. $0$
• B. $\pi$
• C. $2\pi$
• D. $\dfrac{\pi}{4}$