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Solving a Trigonometric Integral

pape

New member
Sep 15, 2013
4
Can anyone please help to solve this following integral?
∫(sin(x)-sin^2 (x)/√(sin^2 (x)+c)) dx
c is a constant
 

Petrus

Well-known member
Feb 21, 2013
739
Re: integral

Can anyone please help to solve this following integral?
∫(sin(x)-sin^2 (x)/√(sin^2 (x)+c)) dx
c is a constant
Integral belongs to calculus...
is this what you want to integrate?
\(\displaystyle \int\frac{\sin(x)-\sin^2(x)}{\sqrt{\sin^2(x)}}+c\)

Regards,
\(\displaystyle |\pi\rangle\)
 

pape

New member
Sep 15, 2013
4
Re: integral

forum.JPG
Please check the JPG file for the correct expression of
the function.

Best...
 
Last edited:

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,123
Re: integral

View attachment 1302
Please check the JPG file for the correct expression of
the function.

Best...
"And what I have found so far is" What is "what you have found"? How did you get this line? What does it mean?

How does the derivative relate to the given problem?

Please be more specific.

-Dan
 

pape

New member
Sep 15, 2013
4
Re: integral

"And what I have found so far is" What is "what you have found"? How did you get this line? What does it mean?

How does the derivative relate to the given problem?

Please be more specific.

-Dan
integral.JPG

Please check the attached file.
I hope that I have been more specific this time.

Regards
 

eddybob123

Active member
Aug 18, 2013
76
Re: integral

You can start by substituting $u=\sin(x)$ to obtain
$$\int u-\frac{u^2}{\sqrt{u^2+c}}\, du$$
From there you can try integration by parts.
 

Petrus

Well-known member
Feb 21, 2013
739
Re: integral

You can start by substituting $u=\sin(x)$ to obtain
$$\int u-\frac{u^2}{\sqrt{u^2+c}}\, du$$
From there you can try integration by parts.
If \(\displaystyle u= \sin(x)\) Then \(\displaystyle du=\cos(x)\,dx\) which is not same as that function he wants to integrate?

Regards,
\(\displaystyle |\pi\rangle\)
 

pape

New member
Sep 15, 2013
4
Re: integral

You can start by substituting $u=\sin(x)$ to obtain
$$\int u-\frac{u^2}{\sqrt{u^2+c}}\, du$$
From there you can try integration by parts.
Hello,
Integration by part leads to a more complicated expression at the end for the finding of the primitive.
Do you have any other suggestion please?

Regards
 

DreamWeaver

Well-known member
Sep 16, 2013
337
Re: integral

Hello,
Integration by part leads to a more complicated expression at the end for the finding of the primitive.
Do you have any other suggestion please?

Regards



Unfortunately, that's because the primitive is quite complex...

Incidentally, if you apply Eddybob's method, but set \(\displaystyle c=b^2\,\), so that \(\displaystyle b=\sqrt{c}\,\), you can take the constant outside of the square root... ;)