Integral \int_0^y dx \frac{\sin(ax+\frac bx)}{x}

siutulysr5

siutulysr5

Answered question

2022-01-24

Integral 0ydxsin(ax+bx)x

Answer & Explanation

Allison Compton

Allison Compton

Beginner2022-01-25Added 16 answers

I would enjoy to have a special function for that.
The only thing I have in mind is to simplify the problem using x=ya and c=ab to make
sin(ax+bx)xdx=sin(y+cy)ydy
and then expand the integrand as a series built at c=0 to get
sin(y+cy)y=n=0sin(y+nπ2)yn+1n!cn
and then use
sinyykdy=12yk((iy)kΓ(1k,iy)+(iy)kΓ(1k,iy))
cosyykdy=12iyk((iy)kΓ(1k,iy)(iy)kΓ(1k,iy))

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?