∫sin^2x/(1+sin^2x )dx求解,
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∫sin^2x/(1+sin^2x)dx求解,∫sin^2x/(1+sin^2x)dx求解,∫sin^2x/(1+sin^2x)dx求解,原式=∫[1-1/(2sin²x+cos²
∫sin^2x/(1+sin^2x )dx求解,
∫sin^2x/(1+sin^2x )dx求解,
∫sin^2x/(1+sin^2x )dx求解,
原式=∫[1-1/(2sin²x+cos²x)]dx
=∫dx - ∫[sec²x/(2tan²x+1)]dx
=∫dx - ∫1/[(√2tanx)²+1)]d(tanx)
=∫dx - √2/2* ∫1/[(√2tanx)²+1)]d(√2tanx)
=x - ∫dx - √2/2*arctan(√2tanx)+c
∫sin^2x/(1+sin^2x )dx
=∫（(1+sin^2x )-1）/(1+sin^2x )
=x-1/(1+sin^2x )
=x-1/(cos^2x +2sin^2x )√
=x-csc^2x /(cot^2x +2)
=x+（1/√2）argtan（cot^2x /√2）
原式=∫[1-1/(2sin²x+cos²x)]dx
=∫dx - ∫[sec²x/(2tan²x+1)]dx
=∫dx - ∫1/[(√2tanx)²+1)]d(tanx)
=∫dx - √2/2* ∫1/[(√2tanx)²+1)]d(√2tanx)
=x-√2/2*arctan(√2tanx)+c
∫sin^2x/(1+sin^2x )dx求解,
∫(1/sin^2x+1)d(sinx)=
x*（1+sin^2 x )/sin^2x 不定积分
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1/sin^2x的不定积分谢谢!（是1/sin x * sin x）