Mathematics

# Find integrals of given function; $\displaystyle \int{{e^{\sqrt x }}} \sqrt x dx =$

##### SOLUTION
$\displaystyle =\int e^{\sqrt{x}}\sqrt{x}dx$

$\sqrt{x}=t$    $x=t^{2}$

$\dfrac{dx}{2\sqrt{x}}=dt$      $\dfrac{\sqrt{x}dx}{2x}=dt\sqrt{x}=2xdt=2t^{2}dt$
$=\displaystyle \int 2t^{2}e^{t}dt$

$=\displaystyle 2\left[t^{2}e^{t}-\int 2te^{t}dt\right]$
$=\displaystyle 2\left[t^{2}e^{t}-2te^{t}+2\int e^{t}dt\right]$

$=2\left[t^{2}e^{t}-2te^{t}+2e^{t}\right]+C$

put $t=\sqrt{x}$

$=2xe^{\sqrt{x}}-4\sqrt{x}e^{\sqrt{x}}+4e^{\sqrt{x}}+C$.

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

#### Realted Questions

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Evaluate $\displaystyle\int^{\frac{3}{2}}_{-1}|x\sin(\pi x)|dx$.
• A. $3\pi +\pi^2$
• B. $\dfrac { 2 }{ \pi } +\dfrac { 1 }{ { \pi }^{ 2 } }$
• C. none of the above
• D. $\dfrac {3}{\pi} +\dfrac {1}{\pi^2}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\int { { e }^{ x }\left( \dfrac { 1-\sin { x } }{ 1-\cos { x } } \right) dx }$ is equal to
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• C. $\dfrac { 1 }{ 2 } { e }^{ x }\cot { \left( \dfrac { x }{ 2 } \right) } +C$
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1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
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Evaluate the given integral.
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