CK-12-Calculus

http://www.ck12.org Chapter 7. Integration Techniques

∫

excosxdx=exsinx−

[

−excosx−

∫

(−cosx)(exdx)

]

=exsinx−excosx−

∫

excosxdx.

Notice that the unknown integral now appears on both sides of the equation. We can simply move the unknown
integral on the right to the left side of the equation, thus adding it to our original integral:

2

∫

excosxdx=exsinx+excosx+C.

Dividing both sides by 2,we obtain

∫

excosxdx=^12 exsinx+^12 excosx+^12 C.

Since the constant of integration is just a “dummy” constant, letC 2 →C.
Finally, our solution is

∫

excosxdx=^12 exsinx+^12 excosx+C.

Multimedia Links

To see this same "classic" example worked out with narration17.0, see Khan Academy Indefinite Integration Series
Part 7 (9:38).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/595

For additional video presentations on integration by parts17.0, see Math Video Tutorials by James Sousa, Integra
tion by Parts, Basic (7:08)

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/596