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Problem:

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

Progress so far:

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

[tex]\frac{1}{8} \int (1-cos2x)^3 dx [/tex]

[tex]\frac 1 8 \int (1 - 3cos2x + 3cos^22x - cos^32x) dx[/tex]

Any help is appreciated.

I can see using a half angle identity for cos^2(2x), but what do I do with the cos^3(2x)?

Steve

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

Progress so far:

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

[tex]\frac{1}{8} \int (1-cos2x)^3 dx [/tex]

[tex]\frac 1 8 \int (1 - 3cos2x + 3cos^22x - cos^32x) dx[/tex]

Any help is appreciated.

I can see using a half angle identity for cos^2(2x), but what do I do with the cos^3(2x)?

Steve

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