求不定积分,求大佬
1个回答
2017-11-30
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降次
∫sin^4θdθ
=∫(sin²θ)²dθ
=∫(1-cos2θ)²/4dθ
=1/4∫(1-2cos2θ+cos²2θ)dθ
=1/4∫dθ-1/4∫cos2θd(2θ)+1/4∫(1+cos4θ)/2dθ
=1/4θ-1/4sin2θ+1/8∫dθ+1/32∫cos4θd(4θ)
=3/8θ-1/4sin2θ+1/32sin4θ+C
∫sin^4θdθ
=∫(sin²θ)²dθ
=∫(1-cos2θ)²/4dθ
=1/4∫(1-2cos2θ+cos²2θ)dθ
=1/4∫dθ-1/4∫cos2θd(2θ)+1/4∫(1+cos4θ)/2dθ
=1/4θ-1/4sin2θ+1/8∫dθ+1/32∫cos4θd(4θ)
=3/8θ-1/4sin2θ+1/32sin4θ+C
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