integration problem

[nappa]

im trying to integrate cosx/((sinx)^2(cos2x+3(sinx)^2)) i tried converting the sinx*2 to 1-cosx^2 but i got lost in my math and even tried to use the (1+cos2x)/2 and still im lost can anyone help please

 

[Deleted member 4993]

im trying to integrate cosx/((sinx)^2(cos2x+3(sinx)^2)) i tried converting the sinx*2 to 1-cosx^2 but i got lost in my math and even tried to use the (1+cos2x)/2 and still im lost can anyone help please

Is your problem:

\(\displaystyle \displaystyle \frac{cos(x)}{sin^2(x)} \ * \ [cos(2x) + 3*sin^2(x)]\)

Then

\(\displaystyle = \displaystyle \frac{cos(x)}{sin^2(x)} \ * \ [1 - 2*sin^2(x) + 3*sin^2(x)]\)

\(\displaystyle = \displaystyle \frac{cos(x)}{sin^2(x)} \ * \ [1 + sin^2(x)]\)

\(\displaystyle = \displaystyle \frac{cos(x)}{sin^2(x)} \ + \ cos(x)\)

Where exactly did you get lost?

 

[nappa]

no my problem is where the cosx is over all the rest somewhat like this

[FONT=MathJax_Math]c[/FONT][FONT=MathJax_Math]o[/FONT][FONT=MathJax_Math]s[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])/sin^2x [/FONT][FONT=MathJax_Main]∗1/[/FONT][FONT=MathJax_Main][[/FONT][FONT=MathJax_Math]cos2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]∗[/FONT][FONT=MathJax_Math]s[/FONT][FONT=MathJax_Math]i[/FONT][FONT=MathJax_Math]n^[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]][/FONT]

 

[Deleted member 4993]

no my problem is where the cosx is over all the rest somewhat like this

[FONT=MathJax_Math]c[/FONT][FONT=MathJax_Math]o[/FONT][FONT=MathJax_Math]s[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])/sin^2x [/FONT][FONT=MathJax_Main]∗1/[/FONT][FONT=MathJax_Main][[/FONT][FONT=MathJax_Math]cos2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]3[/FONT][FONT=MathJax_Main]∗[/FONT][FONT=MathJax_Math]s[/FONT][FONT=MathJax_Math]i[/FONT][FONT=MathJax_Math]n^[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]][/FONT]

Then is your problem:

\(\displaystyle \displaystyle \frac{cos(x)}{sin^2(x)*\frac{1}{cos(2x)+3sin^2(x)}}\)

or

\(\displaystyle \displaystyle \frac{cos(x)}{sin^2(x) \ * \ [cos(2x)+3sin^2(x)]}\)

 

[nappa]

the question was the second choice but my teacher help me to solve it. But thank you for the help. Sorry about that