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autodidude
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Homework Statement
Integrate [tex]\frac{xe^{2x}}{(1+2x)^2}[/tex] with respect to x
Didn't get anywhere with integration by parts or substitution using u=xe^(2x)
A push in the right direction would be much appreciated.
autodidude said:Ok, I now have the following:
[tex]\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}[/tex]
autodidude said:Homework Statement
Integrate [tex]\frac{xe^{2x}}{(1+2x)^2}[/tex] with respect to x
Didn't get anywhere with integration by parts or substitution using u=xe^(2x)
A push in the right direction would be much appreciated.
ehild said:Integrate by parts
∫uv'dx=uv-∫u'vdx,
using u=xe2x and v'=1/(1+2x)2.
ehild
The formula for integrating (xe^(2x))/(1+2x)^2 is given by:
∫ (xe^(2x))/(1+2x)^2 dx = (e^(2x)(2x^2+4x+1))/(4(1+2x)) + C
To simplify the integrated form of (xe^(2x))/(1+2x)^2, you can use partial fractions and break the expression into simpler fractions.
Yes, you can solve the integral of (xe^(2x))/(1+2x)^2 using substitution. Let u = 1+2x, then du/dx = 2 and dx = du/2. By substituting these values, the integral can be simplified.
There is no specific shortcut or trick to solving the integral of (xe^(2x))/(1+2x)^2. However, using different methods such as substitution, partial fractions, or integration by parts can make the process easier.
The integral of (xe^(2x))/(1+2x)^2 is used in various fields of science and engineering, such as physics, chemistry, and economics. It can be used to solve problems related to growth and decay, motion, and optimization.