Quick question on integral distribution

[frasifrasi]

So one example in my book goes from this step:

Integral of[1/4 + cos2x/2 + 1/4((1+cos4x)/2)] dx

to

= 3/8Integral dx + 1/4integral 2cos2xdx + 1/32integral 4cos4x dx

I am very confused as to why, in the process od destribution, the integral became 3/8intdx as opposed to just int 1/4dx and so forth... Where did that 3/8 come form?

Thank you!

 

[Astronuc]

Integral of[1/4 + cos2x/2 + 1/4((1+cos4x)/2)] dx

Expand the third term and regroup terms of dx, cos 2x dx, cos 4x dx

 

[HallsofIvy]

So one example in my book goes from this step:

Integral of[1/4 + cos2x/2 + 1/4((1+cos4x)/2)] dx

to

= 3/8Integral dx + 1/4integral 2cos2xdx + 1/32integral 4cos4x dx

I am very confused as to why, in the process od destribution, the integral became 3/8intdx as opposed to just int 1/4dx and so forth... Where did that 3/8 come form?

Thank you!

3/8= 1/4+ 1/8. The 1/4 is the first term and the 1/8 is from the last term.