求不定积分（2+x-x^2)^1/2dx

来源：学生作业帮助网编辑：作业帮时间：2024/11/16 19:28:50

求不定积分（2+x-x^2)^1/2dx
求不定积分（2+x-x^2)^1/2dx

求不定积分（2+x-x^2)^1/2dx
令 x﹣1/2 = (3/2) sint,dx = (3/2) cost dt
| = ∫ (9/4) cos²t dt
= 9/8 ∫ (1+ cos2t) dt
= (9/8) { t + (1/2)sin2t } + C
= (9/8) arcsin(2x-1)/3 + (1/2) (x-1/2) √(2+x﹣x²) + C

积分:[(9/4)-(x-1/2)^2]^(1/2) dx
=sin^(-1)((x-1/2)/(3/2))
=sin^(-1)((2x-1)/3)

求不定积分dx/x^2 不定积分符号[(x+1)/x^2+xlnx]dx,求不定积分求不定积分dx/（1+x^2)^(2) sin(x^1/2)dx 求不定积分求不定积分(arctanx)/(1+x^2) dx 求不定积分1/x^2dx ∫(x-1)^2dx,求不定积分, 求∫(2x+1)dx不定积分求不定积分x( sin^2)x dx 求不定积分dx/x^2-x+6 dx/(4x-x^2)求不定积分求不定积分 ∫x/(x^2)dx 求不定积分x+1/x^2+2x+3×dx 求dx/[(x-1)(x^2+4x+9)]不定积分? 求不定积分:∫[x(e^x)]/[(1+x)^2]dx 求不定积分(3-x)/根号(1+x+x^2)dx 求不定积分∫(x^2-3x)/(x+1)dx 不定积分 x*sqrt(x+x^2) dx求不定积分 x*sqrt(x+x^2) dx