Integrate the function frac{x}{e^{x^{2}}}. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To integrate the function $I = \int \frac{x}{e^{x^{2}}} dx$,we use the method of substitution.Let $x^{2} = t$.Differentiating both sides with resp

Vedclass · Accepted Answer

$-\frac{1}{2} e^{-x^{2}} + C$

Vedclass · Answer

(A) To integrate the function $I = \int \frac{x}{e^{x^{2}}} dx$,we use the method of substitution.Let $x^{2} = t$.Differentiating both sides with respect to $x$,we get $2x dx = dt$,which implies $x dx = \frac{1}{2} dt$.Substituting these into the integral:$I = \int \frac{1}{e^{t}} \cdot \frac{1}{2} dt$$I = \frac{1}{2} \int e^{-t} dt$Integrating $e^{-t}$ with respect to $t$ gives $-e^{-t}$:$I = \frac{1}{2} (-e^{-t}) + C$$I = -\frac{1}{2} e^{-t} + C$Substituting back $t = x^{2}$:$I = -\frac{1}{2} e^{-x^{2}} + C = -\frac{1}{2e^{x^{2}}} + C$,where $C$ is an arbitrary constant.

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

Similar Questions

If $\int \frac{\sin 2 x}{(a+b \cos x)^{2}} d x=\alpha\left[\log _{e}|a+b \cos x|+\frac{a}{a+b \cos x}\right]+c$,then $\alpha=$

Integrate the function $\frac{\cos \sqrt{x}}{\sqrt{x}}$.

$\int {{e^{3\log x}}{{({x^4} + 1)}^{ - 1}}\,dx} = $

If $f(x) = \frac{1}{(\cos^2 x) \sqrt{1 + \tan x}}$,then its anti-derivative $F(x) = . . . . . . .$,given $F(0) = 4$.

$\int \frac{e^{2x}}{\sqrt[4]{e^x+1}} dx =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module