Re: 微積
※ 引述《nothinger (小魚)》之銘言：
: ∫(secx)^3(tanx)^10dx
Use the identity (tanx)^2 = (secx)^2 - 1, we have
∫(secx)^3 [(secx)^2 - 1]^2 dx. Then the reduction formula for integral
∫(secx)^n dx = ∫(secx)^(n-2) (secx)^2 dx with integration by parts
gives the desired result.
: ∫(sinx)^10(cosx)^30dx
Use half-angle formula, we have (sinx)^2 = (1 - cos2x)/2 and
(cosx)^2 = (1 + cos2x)/2. By binomial theorem and substitution method,
of integral, we are done.
: how to do these?
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