搜搜考试网高等数学微积分,定积分
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高等数学微积分,定积分
19 ∫(x-1)dx/(x^2+x+1) = (1/2)∫(2x+1-3)dx/(x^2+x+1)
= (1/2)∫(2x+1)dx/(x^2+x+1) - (3/2)∫dx/(x^2+x+1)
= (1/2)ln(x^2+x+1) - (3/2)∫dx/[(x+1/2)^2+x+3/4]
= (1/2)ln(x^2+x+1) - √3∫d[(2x+1)/√3]/{1+[(2x+1)/√3]^2}
= (1/2)ln(x^2+x+1) - √3arctan[(2x+1)/√3] + C.
20 ∫dx/(cosx+sinx) = √2∫d(x-π/4)/cos(x-π/4)
= √2ln|sec(x-π/4)+tan(x-π/4)| + C
= (1/2)∫(2x+1)dx/(x^2+x+1) - (3/2)∫dx/(x^2+x+1)
= (1/2)ln(x^2+x+1) - (3/2)∫dx/[(x+1/2)^2+x+3/4]
= (1/2)ln(x^2+x+1) - √3∫d[(2x+1)/√3]/{1+[(2x+1)/√3]^2}
= (1/2)ln(x^2+x+1) - √3arctan[(2x+1)/√3] + C.
20 ∫dx/(cosx+sinx) = √2∫d(x-π/4)/cos(x-π/4)
= √2ln|sec(x-π/4)+tan(x-π/4)| + C