Hello I have this integral and I can't solve it(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int\csc^6 x dx[/tex]

Well i first start with trig identnity [tex]\csc x = \frac{1}{sen x}[/tex] so my first attempt to slove it looks like this

[tex]\int\frac{dx}{(\sin^2 x)^3}[/tex]

then i subsituted with [tex]\sin^2 x = \frac{1 - \cos 2x}{2}[/tex]

and i get

[tex]8\int\frac{dx}{(1-cos 2x)^3} [/tex] and i saw that i was going to

nowhere so i try another way

i took the function and use the trig identity to get this

[tex]\int\csc^6 x dx[/tex] =[tex]\int \frac{\sec^6 x}{\tan^6 x} dx [/tex]

[tex]u = \tan x[/tex] [tex]du = \sec^2 x[/tex]

then

[tex]\int\frac{du^3}{tan^6 x}[/tex]

and i get stucked again. any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Easy looks integral. Help

**Physics Forums | Science Articles, Homework Help, Discussion**