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ggrree

  • 2 years ago

integral of: tan^78 (x) * sec^4 (x)

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  1. badreferences
    • 2 years ago
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    Is... that tan(x)^78? Good... Gods...

  2. badreferences
    • 2 years ago
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    I'm not doing 78 half angle identity integrals.

  3. ggrree
    • 2 years ago
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    yes :P

  4. ggrree
    • 2 years ago
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    Apparently there's a clever way to do it

  5. badreferences
    • 2 years ago
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    You should make your teacher mad and do 70 half angle identity integrals.

  6. Hermeezey
    • 2 years ago
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    Holy crap! thats a lot Tangents, anways: \[\sec^4x = \sec^2x \sec^2x = (\tan^2x +1)(\sec^2x)\] now use a U-Sub where: \[u=tanx\] \[du=\sec^2x dx\] so now we have: u^78 (u^2 + 1) du distributing the u^78, we get: u^80 - u^78 du now just integrate and we get (1/81) (u^81) + (1/79) (u^79) now plug back in the tanx (1/81) (tan^81x) + (1/79)(tan^79x)

  7. Hermeezey
    • 2 years ago
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    i might have made a mistake somwhere, i mean, THATS A LOT O TANGENTS haha

  8. badreferences
    • 2 years ago
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    Whoa man, that's like, clever. I was thinking also of something clever, like a series representation of each new half angle integral, but your method was by far the best.

  9. Hermeezey
    • 2 years ago
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    Haha I just learned how to integrate the trig stuff so its still fresh in my mind. But I think it would be pretty smart to use a Series representation for each of the half-angles

  10. ggrree
    • 2 years ago
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    That's the right answer. Thanks!

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