Mathematics

# Solve $\displaystyle\int { \dfrac { x }{ \sqrt { x+4 } } dx }$

##### SOLUTION
$\begin{array}{l} \int { \dfrac { x }{ { \sqrt { x+4 } } } dx } \\ putting\, x+4={ t^{ 2 } } \\ dx=2tdt \\ =\int { \dfrac { { { t^{ 2 } }-4 } }{ t } } \times 2tdt \\ =2\int { \left( { { t^{ 2 } }-4 } \right) } dt \\ =2\left[ { \dfrac { { { t^{ 3 } } } }{ 3 } -4t } \right] +c \\ =2\left[ { \dfrac { { { { \left( { x+4 } \right) }^{ 3/2 } } } }{ 3 } -4{ { \left( { x+4 } \right) }^{ 1/2 } } } \right] +c \\ =\dfrac { 2 }{ 3 } { \left( { x+4 } \right) ^{ 3/2 } }-8\sqrt { x+4 } +c \end{array}$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
If $\displaystyle f\left ( x \right )=\int\frac{1}{x-\sqrt{x^{2}+1}}$ and $\displaystyle f\left ( 0 \right )=\frac{1+\sqrt{2}}{2}$, then $f(1)$ is equal to
• A. $\displaystyle \frac {-1}{\sqrt {2}}$
• B. $\displaystyle 1+ \sqrt{2}$
• C. $\displaystyle \dfrac12\log \left ( 1+\sqrt{2} \right )$
• D. $\displaystyle \log \left (\sqrt{ \sqrt{2}-1} \right )$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int \dfrac {\sin 2x}{1+\cos^{4}x}dx$ is equal to
• A. $\sin^{-1}(\cos^{2}x)+c$
• B. $\cot^{-1}(\cos^{2}x)+c$
• C. $None\ of\ these$
• D. $\cos^{-1}(\cos^{2}x)+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int \frac{x\quad dx}{\sqrt{1 + x^{2} + \sqrt{(1 + x^{2})^{3}}}}$ is equal to
• A. $\displaystyle \frac{1}{2} ln (1 + \sqrt{1 + x^{2}}) + c$
• B. $2(1 + \sqrt{1 + x^{2}}) + c$
• C. none of these
• D. $2\sqrt{1 +\sqrt{1 + x^{2}}} + c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate $\sqrt { 1-2x } dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
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.
On the basis of above information answer the following questions