求不定积分1.∫ln(1+x^2)dx2.∫sin根号xdx3.∫(arcsinx)^2dx

∫ln(1+x^2)dx=xln(1+x^2)-2∫x^2/(1+x^2)dx=xln(1+x^2)-2x+2∫1/(1+x^2)dx=xln(1+x^2)-2x+2arctanx+c
∫sin根号xdx =∫sintdt^2=2∫t*sintdt=-2t*cost+2∫costdt=-2t*cost+sint
=-2√xcos√x+sin√x+c
∫(arcsinx)^2dx=∫t^2dsint=sint*t^2-2∫t*sintdt=sint*t^2+2t*cost-sint=x*(arcsinx)^2+2x*√(1-x^2)-x+c
数据没有校正,但方法是对的

1.∫ln(1+x^2)dx =1/2(1+x^2)[ln(1+x^2)+1]+c
2.∫sin根号xdx =-2*tcos(x^(1/2))+2*sin(x^(1/2))+c
3.∫(arcsinx)^2dx=x*(arcsinx)^2+2(1-x^2)^(1/2)arcsinx-2*x+c