Mathematics

# Integrate the function   $\displaystyle \frac {x}{e^{x^2}}$

##### SOLUTION
Put $x^2=t$
$\therefore 2xdx=dt$
$\Rightarrow\displaystyle \int \frac {x}{e^{x^2}}dx=\frac {1}{2}\int \frac {1}{e^t}dt$
$\displaystyle =\frac {1}{2}\int e^{-t}dt$
$\displaystyle =\frac {1}{2}\left (\frac {e^{-t}}{-1}\right )+C$
$\displaystyle =-\frac {1}{2}e^{-x^2}+C$
$\displaystyle =\frac {-1}{2e^{x^2}}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \int \frac{2+\sqrt{x}}{\left ( x+\sqrt{x} +1\right )^{2}}dx$
• A. $\displaystyle \frac{x}{x+\sqrt{x}+1}$
• B. $\displaystyle \frac{2\sqrt{x}}{x+\sqrt{x}+1}$
• C. $\displaystyle \frac{\sqrt{2x}}{x+\sqrt{x}+1}$
• D. $\displaystyle \frac{2x}{x+\sqrt{x}+1}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Integrate $\displaystyle\int \sqrt{\dfrac{\cos x-\cos^3x}{(1-\cos^3x)}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Let $y=f(x)$ be a continuous function such that $(3-x)=f(3+x)\ \forall\ x\ \in\ R$. If $\displaystyle \int^{-2}_{-5}f(x)dx=2\int^{2}_{-2}f(x)dx=3$ and $\displaystyle \int^{4}_{2}f(x)dx=4$ then the value of $\displaystyle \int^{11}_{-5}f(x)dx$ equals
• A. $16$
• B. $14$
• C. $12$
• D. $18$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Evaluate $\int\, \displaystyle \frac {dx}{sin^2\, x\, +\, sin\, 2x}$.
• A. $\, \displaystyle \frac {1}{2}\, ln \left | \displaystyle \frac {cot\, x}{cot\, x+2} \right |\, +\, C$
• B. $\, \displaystyle \frac {1}{2}\, ln \left | \displaystyle \frac {tan\, x}{tan\, x-2} \right |\, +\, C$
• C. $\, \displaystyle \frac {1}{2}\, ln \left | \displaystyle \frac {cot\, x+2}{cot\, x} \right |\, +\, C$
• D. $\, \displaystyle \frac {1}{2}\, ln \left | \displaystyle \frac {tan\, x}{tan\, x+2} \right |\, +\, C$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$