令tanx＝t,则
∫dx/(tan^x+sin^x)＝∫dt/(t^4＋2t^2)＝1/2×∫[1/t^2－1/(t^2+2)]dt＝1/2×[－1/t－1/√2×arctan(t/√2)]＋C
＝－1/2tanx－1/(2√2)×arctan(tanx/√2)＋C
令tanx＝t,则
∫dx/(tan^x+sin^x)＝∫dt/(t^4＋2t^2)＝1/2×∫[1/t^2－1/(t^2+2)]dt＝1/2×[－1/t－1/√2×arctan(t/√2)]＋C
＝－1/2tanx－1/(2√2)×arctan(tanx/√2)＋C