# How to Integrate x.e^x and x^2.e^x

Integrals of the type x.e^{x} are often encountered in engineering subjects, particularly when evaluating coefficients for exponential Fourier series. General Interpretation can be to apply a u.v integration by parts to solve for a solution however if you adopt this approach solution can become considerably long and time consuming.

To avoid this cumbersome integration by parts when solving for ∫ ( x.e^x ) dx a simplified predetermined result can be used to integrate x.e^x to save your time and effort during exams and homework. This result can be memorized easily and its application will make the solution shorter.

so here you go:

a = constant.

__Note:__ This is the same result you will get when integrating x.e^{ax} manually by parts.

#### Solved Example for integration of x.e^{x}

Let's demonstrate this with the help of an example:

### Q: ∫( x.e^{-2x })

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## Integration of x^2 . e^x

Integration of x^{2}.e^{x }can be done in the same way as x.e^{x }using a similar predetermined result, stated below.

a = constant.

__Note:__ This is also the same result you will get when integrating x^{2}.e^{ax} manually by parts.

#### Solved Example for integration of x^{2}.e^{x}

Let's demonstrate this with the help of an example which finds c_{n }for complex Fourier series of x^{2 }using our predetermined result.

### Q: ∫( x^{2}.e^{-jwnx })

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