Mathematics

# Integrate the function $x\sqrt {x+2}$

##### SOLUTION
$\int \sqrt {x+2}dx$
put $x+2=t\Rightarrow x =t-2$

$\displaystyle \int (t-2)\sqrt t (dt)$

$=\int ( t^{3/2}-2t^{1/2}) dt$

$=\dfrac {t^{5/2}}{5/2}-2 \times \dfrac {t^{3/2}}{3/2}=\dfrac 25 (x+2)^{5/2}-\dfrac 43 (x+2)^{3/2}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int _{ 0 }^{ 2\pi }{ \dfrac { x\sin ^{ 2n }{ x } }{ \sin ^{ 2n }{ x } +\cos ^{ 2n }{ x } } } dx$.
• A. $2{\pi}^2$
• B. $4{\pi}^2$
• C. $8{\pi}^2$
• D. ${\pi}^2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate: $\int \dfrac {x + 2}{\sqrt {x^{2} + 5x + 6}} dx.$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium

$\int {\frac{{5x - 2}}{{1 + 2x + {x^2}}}\,dx}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of $\displaystyle \int_{-\pi }^{\pi }\left ( 1-x^{2} \right )\sin x\cos ^{2}xdx$ is
• A. $\displaystyle \pi -\frac{\pi ^{3}}{3}$
• B. $\displaystyle 2\pi -\pi ^{3}$
• C. $\displaystyle \frac{7}{2}-2\pi ^{3}$
• D.

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Evaluate : $\displaystyle \int { \cfrac { \sin x \ dx }{ \sqrt { 4\cos ^{ 2 }{ x } -1 } } }$
• A. $-\cfrac { 1 }{ 3 } \log { \left| 2\cos { x } +\sqrt { 4\cos ^{ 2 }{ x } -1 } \right| } +C$
• B. $-\cfrac { 1 }{ 6 } \log { \left| \cos { x } +\sqrt { 2\cos ^{ 2 }{ x } -1 } \right| } +C$
• C. none of these
• D. $-\cfrac { 1 }{ 2 } \log { \left| 2\cos { x } +\sqrt { 4\cos ^{ 2 }{ x } -1 } \right| } +C\quad$