求积分:∫(sec^2(x))*(tan(x))dx,和(0为下限(开根号pi)/2为上限)∫x*sec(x^2)*tan(x^2)dx

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求积分:∫(sec^2(x))*(tan(x))dx,和(0为下限(开根号pi)/2为上限)∫x*sec(x^2)*tan(x^2)dx
求积分:∫(sec^2(x))*(tan(x))dx,和(0为下限(开根号pi)/2为上限)∫x*sec(x^2)*tan(x^2)dx

求积分:∫(sec^2(x))*(tan(x))dx,和(0为下限(开根号pi)/2为上限)∫x*sec(x^2)*tan(x^2)dx
∫(0→√π/2) sec²x tanx dx
= ∫(0→√π/2) tanx d(tanx)
= (1/2)tan²x:[0→√π/2]
= (1/2)tan²(√π/2)
∫ x sec(x²) tan(x²) dx
= ∫ sec(x²) tan(x²) d(x²/2)
= (1/2)∫ d(sec(x²))
= (1/2)sec(x²) + C