请回答14.16.21题,高数不定积分
1个回答
14.
∫xsinxcosxdx
=1/2 ∫xsin2xdx
=1/2 [-x(cos2x)/2+1/2 ∫cos2xdx]
=-x(cos2x)/4+1/8 sin2x+C
16
xln(x-1)dx = ln(x-1)d(x²
∫xln(x－1)dx
=∫ln(x－1)d(x²
=x²ln(x-1)- ∫x²*[1/(x-1)]dx
∫x²*[1/(x-1)]dx = ∫[x+1+1/(x-1)]dx = 1/2x²+x+ln|x-1| + C
21.
∫（arcsinx)^2dx (用分步积分）
=x(arcsinx)^2-∫2xarcsinx/√(1-x^2)dx
=x(arcsinx)^2+∫arcsinx/√(1-x^2)d(1-x^2)
=x(arcsinx)^2+∫arcsinxd[2√(1-x^2)]
=x(arcsinx)^2+arcsinx*[2√(1-x^2)]-∫[2√(1-x^2)]/√(1-x^2)]dx
=x(arcsinx)^2+arcsinx*[2√(1-x^2)]-∫2dx
=x(arcsinx)^2+arcsinx*[2√(1-x^2)]-2x+C
