灵鹊做题网帮算几道积分题.1.∫2xdx/(1+x)(1+x²)²2.∫dx/(sin²x+tg&s
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帮算几道积分题.
1.∫2xdx/(1+x)(1+x²)²
2.∫dx/(sin²x+tg²x)
3.∫xdx/(1+x)√(1-x-x²)
1
4.∫e^(x/2)dx/√[e^x+e^(-x)]
0
1.∫2xdx/(1+x)(1+x²)²
2.∫dx/(sin²x+tg²x)
3.∫xdx/(1+x)√(1-x-x²)
1
4.∫e^(x/2)dx/√[e^x+e^(-x)]
0
1.∫2*x/((1+x)*(1+x^2)^2)*dx=1/4*(2*x-2)/(1+x^2)+1/4*ln(1+x^2)-1/2*ln(x+1)+C
2.∫1/(sin(x)^2+tan(x)^2)*dx=1/4*tan(1/2*x)-1/4/tan(1/2*x)-1/16*2^0.5*ln((tan(1/2*x)^2+tan(1/2*x)*2^0.5+1)/(tan(1/2*x)^2-tan(1/2*x)*2^0.5+1))-1/4*2^0.5*atan(tan(1/2*x)*2^0.5+1)-1/4*2^0.5*atan(tan(1/2*x)*2^0.5-1)-1/16*2^0.5*ln((tan(1/2*x)^2-tan(1/2*x)*2^0.5+1)/(tan(1/2*x)^2+tan(1/2*x)*2^0.5+1))+C
3.∫x/((1+x)*(1-x-x^0.5)^0.5)*dx=-2*(1-x-x^0.5)^0.5-asin(2/5*5^0.5*(x^0.5+1/2))+2/5*(-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5*(-5*atan((-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5/(20+10*5^0.5)^0.5)+2*atan((-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5/(20+10*5^0.5)^0.5)*5^0.5+5^0.5*atanh(10*(2+5^0.5)*(-2+5^0.5)*(-5^0.5-2+x^0.5)/(-5^0.5+2-x^0.5)/(20+10*5^0.5)^0.5/(-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5))/((-2-2*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5^0.5+5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)/(1+(-5^0.5-2+x^0.5)/(-5^0.5+2-x^0.5))^2)^0.5/(1+(-5^0.5-2+x^0.5)/(-5^0.5+2-x^0.5))/(-2+5^0.5)/(20+10*5^0.5)^0.5+C
4.∫exp(x/2)/(exp(x)+exp(-x))^0.5*dx
2.∫1/(sin(x)^2+tan(x)^2)*dx=1/4*tan(1/2*x)-1/4/tan(1/2*x)-1/16*2^0.5*ln((tan(1/2*x)^2+tan(1/2*x)*2^0.5+1)/(tan(1/2*x)^2-tan(1/2*x)*2^0.5+1))-1/4*2^0.5*atan(tan(1/2*x)*2^0.5+1)-1/4*2^0.5*atan(tan(1/2*x)*2^0.5-1)-1/16*2^0.5*ln((tan(1/2*x)^2-tan(1/2*x)*2^0.5+1)/(tan(1/2*x)^2+tan(1/2*x)*2^0.5+1))+C
3.∫x/((1+x)*(1-x-x^0.5)^0.5)*dx=-2*(1-x-x^0.5)^0.5-asin(2/5*5^0.5*(x^0.5+1/2))+2/5*(-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5*(-5*atan((-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5/(20+10*5^0.5)^0.5)+2*atan((-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5/(20+10*5^0.5)^0.5)*5^0.5+5^0.5*atanh(10*(2+5^0.5)*(-2+5^0.5)*(-5^0.5-2+x^0.5)/(-5^0.5+2-x^0.5)/(20+10*5^0.5)^0.5/(-10-10*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5*5^0.5+5*5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)^0.5))/((-2-2*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2-5^0.5+5^0.5*(-5^0.5-2+x^0.5)^2/(-5^0.5+2-x^0.5)^2)/(1+(-5^0.5-2+x^0.5)/(-5^0.5+2-x^0.5))^2)^0.5/(1+(-5^0.5-2+x^0.5)/(-5^0.5+2-x^0.5))/(-2+5^0.5)/(20+10*5^0.5)^0.5+C
4.∫exp(x/2)/(exp(x)+exp(-x))^0.5*dx
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