Question

FIND the integration of
Xe^x dx.

Answer 1

Hey there!

Solution:


$I = \int x e^{x} dx.$

Now, solving this by "Integration by parts"

$I = x \int e^{x}dx - \int ( \dfrac{d(x)}{dx} . \int e^{x})dx\\ \\ I = x .e^{x} - \int( ( 1 ) .e^{x} ) dx.\\ \\ I = x . e^{x} - \int e^{x}. dx\\ \\ I = x . e^{x} - e^{x} + C \\ \\ x. e^{x} - e^{x} + C$


Where C Is the Arbitrary constant.


Pointsmember:

$\int e^{x} = e^{x}$


#Be Brainly.

Answer 2

$\tt \:i \: = \int \: {xe}^{x} \: dx$

• Please refer the attachment for the answer.

#Akshi❣️