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

Updated on April 11, 2016 The author is a resilient graduate in electrical engineering, and an aspiring professional in the said area.

Integrals of the type x.ex 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: Predetermined result for integration of x.e^x | Source

a = constant.

Note: This is the same result you will get when integrating x.eax manually by parts.

Solved Example for integration of x.ex

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

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Integration of x^2 . e^x

Integration of x2.ex can be done in the same way as x.ex using a similar predetermined result, stated below. Predetermined result for integration of x^2.e^ax. | Source

a = constant.

Note: This is also the same result you will get when integrating x2.eax manually by parts.

Solved Example for integration of x2.ex

Let's demonstrate this with the help of an example which finds cn for complex Fourier series of x2 using our predetermined result.