Elementary vs. Non-Elementary integral battles! (beyond regular calculus)

Integration techniques required: integration by parts, u sub, trig sub, partial fraction, algebra, experience, and patience.
Check out these 8 special functions: • how WolframAlpha defin...
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Battle 1, integral of cos(x^2) vs integral of cos(ln(x)), 1:00
Battle 2, integral of ln(1-x^2) vs integral of ln(1-e^x), 7:55
Battle 3, integral of x^(x/ln(x)) vs integral of x^x, 16:23
Battle 4, integral of x*sqrt(x^3+4) vs integral of x*sqrt(x^4+4), 19:29
Battle 5, integral of x/ln(x) vs integral of ln(x)/x, 32:25
Battle 6, integral of ln(ln(x)) vs integral of sqrt(x*sqrt(x)), 34:00
Battle 7, integral of sqrt(sin(x)) vs integral of sin(sqrt(x)), 36:13
Battle 8, integral of sqrt(tan(x)) vs integral of tan(sqrt(x)), 40:52
Battle 9, integral of tan^-1(x) vs integral of sin^-1(x)/cos^-1(x), 59:13
Battle 10, integral of 1/(1-x^2)^(2/3) vs integral of 1/(1-x^2)^(3/2), 1:04:23
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