https://youtu.be/xk_GKQPWbtI

In this video I go over another example on integration by parts and this time solve the integral of the function e<sup>x</sup>sin(x). This is an interesting example in showing that although applying the integration by parts does not simplify the integral, the fact that we are dealing with trigonometry functions in sin(x) and cos(x), applying the integration by parts simply alternates which trig function we use. This allows us to apply the integration by parts twice to obtain the starting integral of e<sup>x</sup>sin(x) on both sides and thus we can add the two and thus divide by 2 to get the final answer. This is a very useful example on integrating by parts so make sure to watch it!

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# Integration by Parts: Example 4

![Integration by Parts Example 4.jpeg](https://cdn.steemitimages.com/DQmVnAqGiSXWPtQAoL5RYJvmHjP41XXDnQE1MDQqu5Qmpix/Integration%20by%20Parts%20Example%204.jpeg)

**Example:**

![](https://cdn.steemitimages.com/DQmZNr3qkvGULEsPnR92TBEZgiaDdAy91VHFxLXh7VDeWii/image.png)

**Solution:**

Note: An easier method is by using complex numbers and I will do this in a later video.

![](https://cdn.steemitimages.com/DQmTiBb9goQWL9iPjc7xBXxWs1kbrHUZ2SbzSNZsDNXR3f1/image.png)

![](https://cdn.steemitimages.com/DQmQHU1HpfQL26EbDTyorDsoqqxeAnxByB11oNiprkW37E2/image.png)