What is the integral of 2xe^x?

Please help me how to solve this problem.

2 Answers
Feb 24, 2018

#int2xe^xdx=2(xe^x-e^x)+C#

Explanation:

To find:

#int2xe^xdx#

By constant rule

#int2xe^xdx=2intxe^xdx#

Let #I= intxe^xdx#

#int2xe^xdx=2I#

We can integrate using the parts rule

#intudv=uv-intvdu#

Here,

#u=xtodu=dx#

#dv=e^xdxtov=e^x#

Substituting

#intxe^xdx=xe^x-inte^xdx#

#inte^xdx=e^x#

#intxe^xdx=xe^x-e^x#

#I=xe^x-e^x#

#int2xe^xdx=2(xe^x-e^x)+C#

Feb 24, 2018

2xe^(x)-2e^(x)+C

Explanation:

We have: #int(2xe^(x))dx#

This integral can be evaluated using integration by parts.

Let #u=2x Rightarrow frac(du)(dx)=2# and #frac(dv)(dx)=e^(x) Rightarrow v=e^(x)#:

#Rightarrow int(2xe^(x))dx=2xe^(x)-int(2e^(x))dx#

#therefore int(2xe^(x))dx=2xe^(x)-2e^(x)+C#