∫sin^8(x/2)dx

来源：学生作业帮助网编辑：作业帮时间：2024/05/10 14:11:42

∫sin^8(x/2)dx
∫sin^8(x/2)dx

∫sin^8(x/2)dx
∫[sin(x/2)]^8dx=∫[35/128-cosx/4+7cos(2x)/32+cos(4x)/128-cosx(1-(sinx)^2)/4]dx
(应用倍角公式)
=∫[35/128-cosx/4+7cos(2x)/32+cos(4x)/128]dx-∫[cosx(1-(sinx)^2)/4]dx
=35x/128-sinx/4+7sin(2x)/64+sin(4x)/512-∫[(1-(sinx)^2)/4]d(sinx)
=35x/128-sinx/4+7sin(2x)/64+sin(4x)/512-sinx/4+(sinx)^3/12+C (C是常数).

∫sin^8(x/2)dx ∫sin(8x)dx ∫x/sin^2(x) dx ∫sin(x) cos^2(x)dx ∫sin^2x/(1+sin^2x )dx求解, ∫sin(6x)sin(2x)dx=? ∫(2/sin^2x)dx= ∫(1-sin^2( x/2))dx 求∫ sin^2 x/2 dx .. 求不定积分：∫sin(x^2)dx 求不定积分∫sin(x/2)dx ∫[(sin^2)x]dx求不定积分 ∫(cosx／1+sin^2x)dx ∫sinx/(cosx-sin^2x)dx ∫sin(√2x)dx ∫ 4/sin^2x dx ∫sin^2x(1+tanx)dx 求∫sin(x^2)dx