求∫-π/2π/2[sin7x/(1+x10)+1/(1+cosx)]dx．

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问题求∫_-π/2^π/2[sin⁷x/(1+x¹⁰)+1/(1+cosx)]dx．

选项

答案∫_-π/2^π/2[sin⁷x/(1+x¹⁰)+1/(1+cosx)]dx=∫_-π/2^π/21/(1+cosx)-2∫₀^π/21/(1+cosx)dx=2∫₀^π/2sec²x/2d(x/2)=2tanx/2｜₀^π/2=2．

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考研数学二

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