帮忙求一个积分~∫cosα/(d+Rsinα)dα积分变量是α上限是2π下限是0

Question

帮忙求一个积分~
∫cosα/(d+Rsinα)dα 积分变量是α 上限是2π 下限是0

Answer 1

∫cosα/(d+Rsinα)dα
=∫dsinα/(d+Rsinα)
=1/R*∫d(Rsinα)/(d+Rsinα)
=1/R*∫d(d+Rsinα)/(d+Rsinα)
=1/R*ln(d+Rsinα)
=1/R*[ln(d+Rsin2π)-ln(d+Rsin0)]
=1/R*(lnd-lnd)
=0