- #1

twoflower

- 368

- 0

I've been having troubles solving this integral:

[tex]

\int \frac{\sin x.\cos x}{\sin^4 x + x.\cos^4 x} dx

[/tex]

Here's how I tried it:

[tex]

t = \cos x

[/tex]

[tex]

dt = - \sin x dx

[/tex]

[tex]

dx = \frac{dt}{-\sin x}

[/tex]

[tex]

x = \arccos t

[/tex]

[tex]

dx = -\frac{1}{\sqrt{1-t^2}} dt

[/tex]

[tex]

-\frac{1}{\sin x} = -\frac{1}{\sqrt{1-t^2}}

[/tex]

[tex]

\sin x = \sqrt{1-t^2}

[/tex]

[tex]

\int \frac{\sin x.\cos x}{\sin^4 x + x.\cos^4 x} dx = - \int \frac{\cos x}{\sin^4 x + x.\cos^4 x} . \left( -\sin x \right) dx = - \int \frac{t}{\left(1-t^2\right)^2 + t^4.\arccos t} dt

[/tex]

Well, I don't know at all what to do with this now...

Does anybody have any idea?

PS: Why doesn't it insert newline, when I write "\\" in the LaTeX code?