Mathematics

# Evaluate the given integral.$\displaystyle\int{{e}^{\log{\sqrt{x}}}dx}$

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

$=\displaystyle\int{\sqrt{x}\,dx}$

$=\displaystyle\int{{x}^{\frac{1}{2}}\,dx}$

$=\dfrac{{x}^{\frac{1}{2}+1}}{\dfrac{1}{2}+1}+c$

$=\dfrac{{x}^{\frac{3}{2}}}{\dfrac{3}{2}}+c$

$=\dfrac{2}{3}{x}^{\frac{3}{2}}+c$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Solve :
$\displaystyle \int_{0}^{\dfrac {\pi}{2}} \sin^3 xdx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\lim_{n\rightarrow \infty}\dfrac{3}{n}\left\{1+\sqrt{\dfrac{n}{n+3}}+\sqrt{\dfrac{n}{n+6}}+\sqrt{\dfrac{n}{n+9}}+...….+\sqrt{\dfrac{n}{n+3(n-1)}}\right\}=?$
• A. Does not exist
• B. $1$
• C. $3$
• D. $2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard

$\displaystyle \int_{0}^{\pi/2}\sqrt{\cos x}\sin^{5}xdx=$
• A. $\displaystyle \frac{34}{231}$
• B. $\displaystyle \frac{30}{321}$
• C. $\displaystyle \frac{128}{231}$
• D. $\displaystyle \frac{64}{231}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int\frac{(sin^{-1}x)^{3}}{\sqrt{1-x^{2}}}dx=$
• A. $\displaystyle \frac{(sin^{-1}x)^{3}}{3}+c$
• B. $(sin^{-1}x)^{4}+c$
• C. $(sin^{-1}x)^{3}+c$
• D. $\displaystyle \frac{1}{4}(sin^{-1}x)^{4}+c$

$\displaystyle\int\dfrac{\cos x-\sin x}{\sqrt{\sin 2x}}dx$.